-
1
-
-
0033242506
-
Remarks on 3D Boltzmann linear operator without cutoff
-
Alexandre R.: Remarks on 3D Boltzmann linear operator without cutoff. Transp. Th. Stat. Phys. 28-5, 433-473 (1999).
-
(1999)
Transp. Th. Stat. Phys.
, vol.5-28
, pp. 433-473
-
-
Alexandre, R.1
-
2
-
-
0034384258
-
Around 3D Boltzmann operator without cutoff. A New formulation
-
Alexandre R.: Around 3D Boltzmann operator without cutoff. A New formulation. Math. Mod. Num. Anal. 343, 575-590 (2000).
-
(2000)
Math. Mod. Num. Anal.
, vol.343
, pp. 575-590
-
-
Alexandre, R.1
-
3
-
-
0035535150
-
Some solutions of the Boltzmann equation without angular cutoff
-
Alexandre R.: Some solutions of the Boltzmann equation without angular cutoff. J. Stat. Phys. 104, 327-358 (2001).
-
(2001)
J. Stat. Phys.
, vol.104
, pp. 327-358
-
-
Alexandre, R.1
-
4
-
-
33846861108
-
Integral kernel estimates for a linear singular operator linked with Boltzmann equation. Part I: Small singularities 0 < ν < 1
-
Alexandre R.: Integral kernel estimates for a linear singular operator linked with Boltzmann equation. Part I: Small singularities 0 < ν < 1. Indiana Univ. Math. J. 55(6), 1975-2021 (2006).
-
(2006)
Indiana Univ. Math. J.
, vol.55
, Issue.6
, pp. 1975-2021
-
-
Alexandre, R.1
-
5
-
-
79953749528
-
A review of Boltzmann equation with singular kernels
-
Alexandre R.: A review of Boltzmann equation with singular kernels. Kin. Rel. Mod. 2(4), 551-646 (2009).
-
(2009)
Kin. Rel. Mod.
, vol.2
, Issue.4
, pp. 551-646
-
-
Alexandre, R.1
-
6
-
-
0034419017
-
Entropy dissipation and long-range interactions
-
Alexandre R., Desvillettes L., Villani C., Wennberg B.: Entropy dissipation and long-range interactions. Arch. Rat. Mech. Anal. 152, 327-355 (2000).
-
(2000)
Arch. Rat. Mech. Anal.
, vol.152
, pp. 327-355
-
-
Alexandre, R.1
Desvillettes, L.2
Villani, C.3
Wennberg, B.4
-
7
-
-
18844411595
-
Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations.I. Non cutoff and Maxwell cases
-
Alexandre R., ElSafadi M.: Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations. I. Non cutoff and Maxwell cases. Math. Mod. Meth. Appl. Sci. 15, 907-920 (2005).
-
(2005)
Math. Mod. Meth. Appl. Sci.
, vol.15
, pp. 907-920
-
-
Alexandre, R.1
Elsafadi, M.2
-
8
-
-
36849030327
-
Uncertainty principle and regularity for Boltzmann type equations
-
Alexandre R., Morimoto Y., Ukai S., Xu C.-J., Yang T.: Uncertainty principle and regularity for Boltzmann type equations. C. R. Acad. Sci. Paris, Ser. I 345, 673-677 (2007).
-
(2007)
C. R. Acad. Sci. Paris, Ser. I
, vol.345
, pp. 673-677
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
9
-
-
56349126806
-
Uncertainty principle and kinetic equations
-
Alexandre R., Morimoto Y., Ukai S., Xu C.-J., Yang T.: Uncertainty principle and kinetic equations. J. Funct. Anal. 255, 2013-2066 (2008).
-
(2008)
J. Funct. Anal.
, vol.255
, pp. 2013-2066
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
10
-
-
67349285957
-
Regularity of solutions for the Boltzmann equation without angular cutoff
-
Alexandre R., Morimoto Y., Ukai S., Xu C.-J., Yang T.: Regularity of solutions for the Boltzmann equation without angular cutoff. C. R. Math. Acad. Sci. Paris, Ser. I 347(13-14), 747-752 (2009).
-
(2009)
C. R. Math. Acad. Sci. Paris, Ser. I
, vol.347
, Issue.13-14
, pp. 747-752
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
11
-
-
72049095061
-
Local existence for non-cutoff Boltzmann equation
-
Alexandre R., Morimoto Y., Ukai S., Xu C.-J., Yang T.: Local existence for non-cutoff Boltzmann equation. C. R. Math. Acad. Sci. Paris, Ser. I 347(21-22), 1237-1242 (2009).
-
(2009)
C. R. Math. Acad. Sci. Paris, Ser. I
, vol.347
, Issue.21-22
, pp. 1237-1242
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
12
-
-
77956094581
-
Regularizing effect and local existence for non-cutoff Boltzmann equation
-
Alexandre R., Morimoto Y., Ukai S., Xu C.-J., Yang T.: Regularizing effect and local existence for non-cutoff Boltzmann equation. Arch. Rat. Mech. Anal. 198(Issue 1), 39-123 (2010).
-
(2010)
Arch. Rat. Mech. Anal.
, vol.198
, Issue.1
, pp. 39-123
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
13
-
-
84155195145
-
Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential
-
(To appear)
-
Alexandre, R., Morimoto, Y., Ukai, S., Xu, C.-J., Yang, T.: Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential. J. Funct. Anal. http://hal. archives-ouvertes. fr/hal-00496950/fr/ (To appear).
-
J. Funct. Anal
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
14
-
-
79955762339
-
Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
-
(To appear)
-
Alexandre, R., Morimoto, Y., Ukai, S., Xu, C.-J., Yang, T.: Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential. Anal. Appl. http://hal. archives-ouvertes. fr/hal-00510633/fr/, 2010 (To appear).
-
(2010)
Anal. Appl
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
15
-
-
79955748633
-
Qualitative properties of solutions to the Boltzmann equation without angular cutof
-
(To appear)
-
Alexandre, R., Morimoto, Y., Ukai, S., Xu, C.-J., Yang, T.: Qualitative properties of solutions to the Boltzmann equation without angular cutof. Arch. Rational Mech. Anal. (To appear).
-
Arch. Rational Mech. Anal
-
-
Alexandre, R.1
Morimoto, Y.2
Ukai, S.3
Xu, C.-J.4
Yang, T.5
-
16
-
-
0036133764
-
On the Boltzmann equation for long-range interaction
-
Alexandre R., Villani C.: On the Boltzmann equation for long-range interaction. Comm. Pure Appl. Math. 55, 30-70 (2002).
-
(2002)
Comm. Pure Appl. Math.
, vol.55
, pp. 30-70
-
-
Alexandre, R.1
Villani, C.2
-
17
-
-
0019717771
-
Intermolecular forces of infinite range and the Boltzmann equation
-
Arkeryd L.: Intermolecular forces of infinite range and the Boltzmann equation. Arch. Rat. Mech. Anal. 77(1), 11-21 (1981).
-
(1981)
Arch. Rat. Mech. Anal.
, vol.77
, Issue.1
, pp. 11-21
-
-
Arkeryd, L.1
-
18
-
-
0000411415
-
The theory of nonlinear, spatially uniform Boltzmann equation for Maxwell molecules
-
Bobylev A.: The theory of nonlinear, spatially uniform Boltzmann equation for Maxwell molecules. Sov. Sci. Rev. C. Math. Phys. 7, 111-233 (1988).
-
(1988)
Sov. Sci. Rev. C. Math. Phys.
, vol.7
, pp. 111-233
-
-
Bobylev, A.1
-
19
-
-
0032220965
-
A proof of smoothing properties of the positive part of Boltzmann's kernel
-
Bouchut F., Desvillettes L.: A proof of smoothing properties of the positive part of Boltzmann's kernel. Rev. Mat. Iberoam. 14, 47-61 (1998).
-
(1998)
Rev. Mat. Iberoam.
, vol.14
, pp. 47-61
-
-
Bouchut, F.1
Desvillettes, L.2
-
20
-
-
0003427848
-
Kinetic equations and asymptotic theory
-
Paris: Gauthiers-Villars
-
Bouchut, F., Golse, F., Pulvirenti, M.: Kinetic equations and asymptotic theory. Series in Appl. Math., Paris: Gauthiers-Villars, 2000.
-
(2000)
Series In Appl. Math
-
-
Bouchut, F.1
Golse, F.2
Pulvirenti, M.3
-
21
-
-
0003840403
-
On the singularities of the global small solutions of the full Boltzmann equation
-
Boudin L., Desvillettes L.: On the singularities of the global small solutions of the full Boltzmann equation. Monat. für Math. 131, 91-108 (2000).
-
(2000)
Monat. Für Math.
, vol.131
, pp. 91-108
-
-
Boudin, L.1
Desvillettes, L.2
-
23
-
-
0003200990
-
The Mathematical theory of Dilute gases
-
New York: Springer-Verlag
-
Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical theory of Dilute gases. Applied Mathematical Sciences, 106. New York: Springer-Verlag, 1994.
-
(1994)
Applied Mathematical Sciences
, vol.106
-
-
Cercignani, C.1
Illner, R.2
Pulvirenti, M.3
-
24
-
-
78951470972
-
The Gevrey hypoellipticity for a class of kinetic equations Comm
-
doi:10.1080/03605302.2010.507689
-
Chen H., Li W.-X., Xu C.-J.: The Gevrey hypoellipticity for a class of kinetic equations Comm. PDE. 36, 693-728 (2011) doi: 10. 1080/03605302. 2010. 507689.
-
(2011)
PDE.
, vol.36
, pp. 693-728
-
-
Chen, H.1
Li, W.-X.2
Xu, C.-J.3
-
25
-
-
67349220644
-
Smoothing effects for classical solutions of the full Landau equation
-
Chen Y., Desvillettes L., He L.: Smoothing effects for classical solutions of the full Landau equation. Arch. Rat. Mech. Anal. 193, 21-55 (2009).
-
(2009)
Arch. Rat. Mech. Anal.
, vol.193
, pp. 21-55
-
-
Chen, Y.1
Desvillettes, L.2
He, L.3
-
26
-
-
21844483733
-
About the regularization properties of the non cut-off Kac equation
-
Desvillettes L.: About the regularization properties of the non cut-off Kac equation. Commun. Math. Phys. 168, 417-440 (1995).
-
(1995)
Commun. Math. Phys.
, vol.168
, pp. 417-440
-
-
Desvillettes, L.1
-
27
-
-
0030506384
-
Regularization for the non Cutoff 2D Radially Symmetric Boltzmann Equation with a Velocity Dependant Cross Section
-
Desvillettes L.: Regularization for the non Cutoff 2D Radially Symmetric Boltzmann Equation with a Velocity Dependant Cross Section. Trans. Th. Stat. Phy. 25(3-5), 383-394 (1996).
-
(1996)
Trans. Th. Stat. Phy.
, vol.3
, Issue.5-25
, pp. 383-394
-
-
Desvillettes, L.1
-
28
-
-
0031495264
-
Regularization Properties of the 2-Dimensional Non Radially Symmetric Non Cutoff Spatially Homogeneous Boltzmann Equation for Maxwellian Molecules
-
Desvillettes L.: Regularization Properties of the 2-Dimensional Non Radially Symmetric Non Cutoff Spatially Homogeneous Boltzmann Equation for Maxwellian Molecules. Trans. Th. Stat. Phys. 26(3), 341-357 (1997).
-
(1997)
Trans. Th. Stat. Phys.
, vol.26
, Issue.3
, pp. 341-357
-
-
Desvillettes, L.1
-
29
-
-
35348914557
-
About the use of the Fourier transform for the Boltzmann equation. Summer School on "Methods and Models of Kinetic Theory" (M& MKT 2002)
-
Desvillettes, L.: About the use of the Fourier transform for the Boltzmann equation. Summer School on "Methods and Models of Kinetic Theory" (M& MKT 2002). Riv. Mat. Univ. Parma 7(2), 1-99 (2003).
-
(2003)
Riv. Mat. Univ. Parma
, vol.7
, Issue.2
, pp. 1-99
-
-
Desvillettes, L.1
-
30
-
-
67349233256
-
Propagation of Gevrey regularity for solutions of Boltzmann equation for Maxwellian molecules
-
Desvillettes L., Furioli G., Terraneo E.: Propagation of Gevrey regularity for solutions of Boltzmann equation for Maxwellian molecules. Trans. Amer. Math. Soc. 361, 1731-1747 (2009).
-
(2009)
Trans. Amer. Math. Soc.
, vol.361
, pp. 1731-1747
-
-
Desvillettes, L.1
Furioli, G.2
Terraneo, E.3
-
31
-
-
0000278898
-
On the spatially homogeneous Landau equation for hard potentials. Part I: existence, uniqueness and smoothness
-
Desvillettes L., Villani C.: On the spatially homogeneous Landau equation for hard potentials. Part I: existence, uniqueness and smoothness. Comm. Part. Diff. Eqs. 25-1-2, 179-259 (2000).
-
(2000)
Comm. Part. Diff. Eqs.
, vol.2-25
, Issue.1-2
, pp. 179-259
-
-
Desvillettes, L.1
Villani, C.2
-
32
-
-
1642284756
-
Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff
-
Desvillettes L., Wennberg B.: Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff. Comm. Part. Diff. Eqs. 29-1-2, 133-155 (2004).
-
(2004)
Comm. Part. Diff. Eqs.
, vol.2-29
, Issue.1-2
, pp. 133-155
-
-
Desvillettes, L.1
Wennberg, B.2
-
33
-
-
0040700838
-
On a model Boltzmann equation without angular cutoff
-
Desvillettes L., Golse F.: On a model Boltzmann equation without angular cutoff. Diff. Int. Eqs. 13(4-6), 567-594 (2000).
-
(2000)
Diff. Int. Eqs.
, vol.13
, Issue.4-6
, pp. 567-594
-
-
Desvillettes, L.1
Golse, F.2
-
34
-
-
0001089576
-
On the Cauchy problem for Boltzmann equations: global existence and weak stability
-
DiPerna R. J., Lions P. L.: On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. 130, 321-366 (1989).
-
(1989)
Ann. Math.
, vol.130
, pp. 321-366
-
-
Diperna, R.J.1
Lions, P.L.2
-
35
-
-
67651232554
-
Stability of the Boltzmann equation with potential forces on torus
-
Duan R.-J.: Stability of the Boltzmann equation with potential forces on torus. Physica D 238, 1808-1820 (2009).
-
(2009)
Physica D
, vol.238
, pp. 1808-1820
-
-
Duan, R.-J.1
-
36
-
-
47749120667
-
Propagation of singularities in the solutions to the Boltzmann equation near equilibrium
-
Duan R.-J., Li M.-R., Yang T.: Propagation of singularities in the solutions to the Boltzmann equation near equilibrium. Math. Mod. Meth. Appl. Sci. 18, 1093-1114 (2008).
-
(2008)
Math. Mod. Meth. Appl. Sci.
, vol.18
, pp. 1093-1114
-
-
Duan, R.-J.1
Li, M.-R.2
Yang, T.3
-
37
-
-
63849275800
-
A combination of energy method and spectral analysis for study of equations of gas motion
-
Duan R.-J., Ukai S., Yang T.: A combination of energy method and spectral analysis for study of equations of gas motion. Front. Math. China 4(2), 253-282 (2009).
-
(2009)
Front. Math. China
, vol.4
, Issue.2
, pp. 253-282
-
-
Duan, R.-J.1
Ukai, S.2
Yang, T.3
-
38
-
-
84968470266
-
The uncertainty principle
-
Fefferman C.: The uncertainty principle. Bull. Amer. Math. Soc. 9, 129-206 (1983).
-
(1983)
Bull. Amer. Math. Soc.
, vol.9
, pp. 129-206
-
-
Fefferman, C.1
-
39
-
-
0003138434
-
Asymptotic Theory of the Boltzmann Equation II
-
J. A. Laurmann, New York: Academic Press
-
Grad, H.: Asymptotic Theory of the Boltzmann Equation II. In: Rarefied Gas Dynamics, J. A. Laurmann, ed, vol. 1, New York: Academic Press, 1963, pp. 26-59.
-
(1963)
Rarefied Gas Dynamics
, vol.1
, pp. 26-59
-
-
Grad, H.1
-
40
-
-
0013510278
-
-
Providence, RI: Amer. Math. Soc., 1965, editor R. Finn
-
Grad, H.: Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Symp. Appl. Math. Vol. 17, Providence, RI: Amer. Math. Soc., 1965, editor R. Finn, pp. 154-183.
-
Asymptotic Equivalence of the Navier-Stokes and Nonlinear Boltzmann Equations, Proc. Symp. Appl. Math
, vol.17
, pp. 154-183
-
-
Grad, H.1
-
42
-
-
77950530316
-
Global classical solutions of the Boltzmann equation with long range potential
-
Gressman P.-T., Strain R.-M.: Global classical solutions of the Boltzmann equation with long range potential. Proc. Nat. Acad. Sci. U. S. A 107(13), 5744-5749 (2010).
-
(2010)
Proc. Nat. Acad. Sci. U.S.A
, vol.107
, Issue.13
, pp. 5744-5749
-
-
Gressman, P.-T.1
Strain, R.-M.2
-
43
-
-
77950538826
-
-
Preprint, avaliable at, [math. AP], 2010
-
Gressman, P.-T., Strain, R.-M.: Global classical solutions of the Boltzmann equation with long range interations and soft potentials. Preprint 2010, avaliable at http://arXiv. org/abs/1002. 3639v2 [math. AP], 2010.
-
(2010)
Global Classical Solutions of the Boltzmann Equation With Long Range Interations and Soft Potentials
-
-
Gressman, P.-T.1
Strain, R.-M.2
-
45
-
-
0036882740
-
The Landau equation in a periodic box
-
Guo Y.: The Landau equation in a periodic box. Comm. Math. Phys. 231, 391-434 (2002).
-
(2002)
Comm. Math. Phys.
, vol.231
, pp. 391-434
-
-
Guo, Y.1
-
46
-
-
8844227476
-
The Boltzmann equation in the whole space
-
Guo Y.: The Boltzmann equation in the whole space. Indiana Univ. Maths. J. 53(4), 1081-1094 (2004).
-
(2004)
Indiana Univ. Maths. J.
, vol.53
, Issue.4
, pp. 1081-1094
-
-
Guo, Y.1
-
47
-
-
67349194487
-
Regularity of solutions for spatially homogeneous Boltzmann equation without Angular cutoff
-
Huo Z. H., Morimoto Y., Ukai S., Yang T.: Regularity of solutions for spatially homogeneous Boltzmann equation without Angular cutoff. Kin. Rel. Mods. 1, 453-489 (2008).
-
(2008)
Kin. Rel. Mods.
, vol.1
, pp. 453-489
-
-
Huo, Z.H.1
Morimoto, Y.2
Ukai, S.3
Yang, T.4
-
48
-
-
0040943239
-
The Boltzmann equation. I. Uniqueness and local existence
-
Kaniel S., Shinbrot M.: The Boltzmann equation. I. Uniqueness and local existence. Commun. Math. Phys. 59, 65-84 (1978).
-
(1978)
Commun. Math. Phys.
, vol.59
, pp. 65-84
-
-
Kaniel, S.1
Shinbrot, M.2
-
49
-
-
0000834860
-
Compactness in Boltzmann's equation via Fourier integral operators and applications, I, II, and III
-
539-584
-
Lions, P. L.: Compactness in Boltzmann's equation via Fourier integral operators and applications, I, II, and III. J. Math. Kyoto Univ., 34, 391-427, 429-461, 539-584 (1994).
-
(1994)
J. Math. Kyoto Univ
, vol.34
-
-
Lions, P.L.1
-
50
-
-
0001416655
-
On Boltzmann and Landau equations
-
Lions P. L.: On Boltzmann and Landau equations. Philos. Trans. Roy. Soc. London Ser. A 346(1679), 191-204 (1994).
-
(1994)
Philos. Trans. Roy. Soc. London Ser. A
, vol.346
, Issue.1679
, pp. 191-204
-
-
Lions, P.L.1
-
51
-
-
0000927020
-
Regularity and compactness for Boltzmann collision operator without angular cut-off
-
Lions P. L.: Regularity and compactness for Boltzmann collision operator without angular cut-off. C. R. Acad. Sci. Paris Séries I 326, 37-41 (1998).
-
(1998)
C. R. Acad. Sci. Paris Séries I
, vol.326
, pp. 37-41
-
-
Lions, P.L.1
-
52
-
-
1842591085
-
Micro-macro decompositions and positivity of shock profiles
-
Liu T.-P., Yu S.-H.: Micro-macro decompositions and positivity of shock profiles. Commun. Math. Phys. 246(1), 133-179 (2004).
-
(2004)
Commun. Math. Phys.
, vol.246
, Issue.1
, pp. 133-179
-
-
Liu, T.-P.1
Yu, S.-H.2
-
53
-
-
0346498040
-
Energy method for Boltzmann equation
-
Liu T.-P., Yang T., Yu S.-H.: Energy method for Boltzmann equation. Phys. D 188, 178-192 (2004).
-
(2004)
Phys. D
, vol.188
, pp. 178-192
-
-
Liu, T.-P.1
Yang, T.2
Yu, S.-H.3
-
54
-
-
33646896267
-
Nonlinear stability of rarefaction waves for the Boltzmann equation
-
Liu T.-P., Yang T., Yu S.-H., Zhao H.-J.: Nonlinear stability of rarefaction waves for the Boltzmann equation. Arch. Ration. Mech. Anal. 181, 333-371 (2006).
-
(2006)
Arch. Ration. Mech. Anal.
, vol.181
, pp. 333-371
-
-
Liu, T.-P.1
Yang, T.2
Yu, S.-H.3
Zhao, H.-J.4
-
55
-
-
0038161745
-
Direct method for the regularity of the gain term in the Boltzmann equation
-
Lu X. A.: Direct method for the regularity of the gain term in the Boltzmann equation. J. Math. Anal. Appl. 228, 409-435 (1998).
-
(1998)
J. Math. Anal. Appl.
, vol.228
, pp. 409-435
-
-
Lu, X.A.1
-
56
-
-
85008727719
-
The uncertainty principle and hypoelliptic operators
-
Morimoto Y.: The uncertainty principle and hypoelliptic operators. Publ. RIMS Kyoto Univ. 23, 955-964 (1987).
-
(1987)
Publ. RIMS Kyoto Univ.
, vol.23
, pp. 955-964
-
-
Morimoto, Y.1
-
57
-
-
36849004153
-
Estimates for degenerate Schrödinger operators and hypoellipticity for infinitely degenerate elliptic operators
-
Morimoto Y.: Estimates for degenerate Schrödinger operators and hypoellipticity for infinitely degenerate elliptic operators. J. Math. Kyoto Univ. 32, 333-372 (1992).
-
(1992)
J. Math. Kyoto Univ.
, vol.32
, pp. 333-372
-
-
Morimoto, Y.1
-
58
-
-
0141734852
-
The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators
-
Morimoto Y., Morioka T.: The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators. Bull. Sc. Math. 121, 507-547 (1997).
-
(1997)
Bull. Sc. Math.
, vol.121
, pp. 507-547
-
-
Morimoto, Y.1
Morioka, T.2
-
59
-
-
79955747406
-
Gevrey smoothing effect of solutions for spatially homogeneous nonlinear Boltzmann equation without angular cutoff
-
Morimoto Y., Ukai S.: Gevrey smoothing effect of solutions for spatially homogeneous nonlinear Boltzmann equation without angular cutoff. J. Pseudo-Dier. Oper. Appl. 1, 139-159 (2010).
-
(2010)
J. Pseudo-Dier. Oper. Appl.
, vol.1
, pp. 139-159
-
-
Morimoto, Y.1
Ukai, S.2
-
60
-
-
67349239513
-
Regularity of solutions to the spatially homogeneous Boltzmann equation without Angular cutoff
-
Morimoto Y., Ukai S., Xu C.-J., Yang T.: Regularity of solutions to the spatially homogeneous Boltzmann equation without Angular cutoff. Disc. Cont. Dyn. Sys. Series A 24(1), 187-212 (2009).
-
(2009)
Disc. Cont. Dyn. Sys. Series A
, vol.24
, Issue.1
, pp. 187-212
-
-
Morimoto, Y.1
Ukai, S.2
Xu, C.-J.3
Yang, T.4
-
61
-
-
35348971478
-
Hypoelliticity for a class of kinetic equations
-
Morimoto Y., Xu C.-J.: Hypoelliticity for a class of kinetic equations. J. Math. Kyoto Univ. 47, 129-152 (2007).
-
(2007)
J. Math. Kyoto Univ.
, vol.47
, pp. 129-152
-
-
Morimoto, Y.1
Xu, C.-J.2
-
62
-
-
33748450509
-
Explicit coercivity estimates for the linearized Boltzmann and Landau operators
-
Mouhot C.: Explicit coercivity estimates for the linearized Boltzmann and Landau operators. Commun. Part. Diff. Eqs. 31, 1321-1348 (2006).
-
(2006)
Commun. Part. Diff. Eqs.
, vol.31
, pp. 1321-1348
-
-
Mouhot, C.1
-
63
-
-
34248226318
-
Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
-
Mouhot C., Strain R. M.: Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff. J. Math. Pures Appl. (9) 87(5), 515-535 (2007).
-
(2007)
J. Math. Pures Appl. (9)
, vol.87
, Issue.5
, pp. 515-535
-
-
Mouhot, C.1
Strain, R.M.2
-
64
-
-
84980156986
-
Boltzmann collision operator with inverse power intermolecular potential, I, II. Commun
-
Pao, Y. P.: Boltzmann collision operator with inverse power intermolecular potential, I, II. Commun. Pure Appl. Math. 27, 407-428, 559-581 (1974).
-
(1974)
Pure Appl. Math
, vol.27
-
-
Pao, Y.P.1
-
65
-
-
33749987309
-
The Vlasov-Maxwell-Boltzmann system in the whole space
-
Strain R. M.: The Vlasov-Maxwell-Boltzmann system in the whole space. Commun. Math. Phys. 268(2), 543-567 (2006).
-
(2006)
Commun. Math. Phys.
, vol.268
, Issue.2
, pp. 543-567
-
-
Strain, R.M.1
-
66
-
-
37449012365
-
Exponential decay for soft potentials near Maxwellian. Arch
-
Strain R., Guo Y.: Exponential decay for soft potentials near Maxwellian. Arch. Rat. Mech. Anal. 187(2), 287-339 (2008).
-
(2008)
Rat. Mech. Anal.
, vol.187
, Issue.2
, pp. 287-339
-
-
Strain, R.1
Guo, Y.2
-
67
-
-
0000824099
-
On the existence of global solutions of mixed problem for non-linear Boltzmann equation
-
Ukai S.: On the existence of global solutions of mixed problem for non-linear Boltzmann equation. Proc. Japan Acad. 50, 179-184 (1974).
-
(1974)
Proc. Japan Acad.
, vol.50
, pp. 179-184
-
-
Ukai, S.1
-
68
-
-
0009328610
-
Les solutions globales de l'equation de Boltzmann dans l'espace tout entier et dans le demi-espace
-
Paris Ser. A-B 282
-
Ukai, S.: Les solutions globales de l'equation de Boltzmann dans l'espace tout entier et dans le demi-espace. C. R. Acad. Sci. Paris Ser. A-B 282 (1976), no. 6, Ai, A317-A320.
-
(1976)
C. R. Acad. Sci
, Issue.6
-
-
Ukai, S.1
-
69
-
-
0003244114
-
Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff
-
Ukai S.: Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff. Japan J. Appl. Math. 1-1, 141-156 (1984).
-
(1984)
Japan J. Appl. Math.
, vol.1
, Issue.1
, pp. 141-156
-
-
Ukai, S.1
-
70
-
-
77957066266
-
Solutions of the Boltzmann equation
-
M. Mimura, T. Nishida, Studies of Mathematics and Its Applications 18, Tokyo: Kinokuniya-North-Holland
-
Ukai, S.: Solutions of the Boltzmann equation In: Pattern and Waves - Qualitative Analysis of Nonlinear Differential Equations eds. M. Mimura, T. Nishida, Studies of Mathematics and Its Applications 18, Tokyo: Kinokuniya-North-Holland, 1986, pp. 37-96.
-
(1986)
Pattern and Waves Qualitative Analysis of Nonlinear Differential Equations
, pp. 37-96
-
-
Ukai, S.1
-
71
-
-
0032338727
-
On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
-
Villani C.: On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arch. Rat. Mech. Anal. 143, 273-307 (1998).
-
(1998)
Arch. Rat. Mech. Anal.
, vol.143
, pp. 273-307
-
-
Villani, C.1
-
72
-
-
0033240596
-
Regularity estimates via entropy dissipation for the spatially homogeneous Boltzmann equation
-
Villani C.: Regularity estimates via entropy dissipation for the spatially homogeneous Boltzmann equation. Rev. Mat. Iberoam. 15(2), 335-352 (1999).
-
(1999)
Rev. Mat. Iberoam.
, vol.15
, Issue.2
, pp. 335-352
-
-
Villani, C.1
-
73
-
-
0038413035
-
A review of mathematical topics in collisional kinetic theory
-
S. Friedlander and D. Serre (Eds.), NorthHolland: Amsterdem
-
Villani C.: A review of mathematical topics in collisional kinetic theory. In: Friedlander, S., Serre, D. (eds) Handbook of Mathematical Fluid Mechanics, pp. 1-1. Amsterdem, NorthHolland (2002).
-
(2002)
Handbook of Mathematical Fluid Mechanics
, pp. 1-1
-
-
Villani, C.1
-
74
-
-
70149105057
-
Convergence rate for the Boltzmann and Landau equations with soft potentials
-
Yu, H.: Convergence rate for the Boltzmann and Landau equations with soft potentials. Proc. Royal Soc. Edinburgh 139A, 393-416 (2009).
-
(2009)
Proc. Royal Soc. Edinburgh
, vol.139 A
, pp. 393-416
-
-
Yu, H.1
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