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Volumn 247, Issue 2, 2009, Pages 596-617

Ultra-analytic effect of Cauchy problem for a class of kinetic equations

Author keywords

Fokker Planck equation; Landau equation; Ultra analytic effect of Cauchy problem

Indexed keywords


EID: 67349092273     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2009.01.028     Document Type: Article
Times cited : (65)

References (21)
  • 2
    • 18844411595 scopus 로고    scopus 로고
    • Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations. I. Non cutoff case and Maxwellian molecules
    • Alexandre R., and Safadi M. Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations. I. Non cutoff case and Maxwellian molecules. Math. Models Methods Appl. Sci. 15 (2005) 907-920
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 907-920
    • Alexandre, R.1    Safadi, M.2
  • 3
    • 67349205234 scopus 로고    scopus 로고
    • Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations. II. Non cutoff and non Maxwell cases
    • Alexandre R., and Safadi M. Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations. II. Non cutoff and non Maxwell cases. Discrete Contin. Dyn. Syst. Ser. A 24 1 (2009) 1-11
    • (2009) Discrete Contin. Dyn. Syst. Ser. A , vol.24 , Issue.1 , pp. 1-11
    • Alexandre, R.1    Safadi, M.2
  • 4
    • 55249097148 scopus 로고    scopus 로고
    • The Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations
    • Chen H., Li W.-X., and Xu C.-J. The Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations. J. Differential Equations 246 1 (2009) 320-339
    • (2009) J. Differential Equations , vol.246 , Issue.1 , pp. 320-339
    • Chen, H.1    Li, W.-X.2    Xu, C.-J.3
  • 5
    • 67349216446 scopus 로고    scopus 로고
    • Gevrey class regularity for the solution of the spatially homogeneous Landau equation
    • Chen H., Li W., and Xu C.-J. Gevrey class regularity for the solution of the spatially homogeneous Landau equation. Kinetic Related Models 1 3 (2008) 355-368
    • (2008) Kinetic Related Models , vol.1 , Issue.3 , pp. 355-368
    • Chen, H.1    Li, W.2    Xu, C.-J.3
  • 6
    • 67349220644 scopus 로고    scopus 로고
    • Smoothing effects for classical solutions of the full Landau equation
    • in press
    • Y. Chen, L. Desvillettes, L. He, Smoothing effects for classical solutions of the full Landau equation, Arch. Ration. Mech. Anal., in press
    • Arch. Ration. Mech. Anal
    • Chen, Y.1    Desvillettes, L.2    He, L.3
  • 7
    • 63449105705 scopus 로고    scopus 로고
    • Smoothness of classical solutions to the Vlasov-Poisson-Landau system
    • Chen Y. Smoothness of classical solutions to the Vlasov-Poisson-Landau system. Kinetic Related Models 1 3 (2008) 369-386
    • (2008) Kinetic Related Models , vol.1 , Issue.3 , pp. 369-386
    • Chen, Y.1
  • 8
    • 67349233256 scopus 로고    scopus 로고
    • Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules
    • Desvillettes L., Furiolo G., and Terraneo E. Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules. Trans. Amer. Math. Soc. 361 (2009) 1731-1747
    • (2009) Trans. Amer. Math. Soc. , vol.361 , pp. 1731-1747
    • Desvillettes, L.1    Furiolo, G.2    Terraneo, E.3
  • 9
    • 0000278898 scopus 로고    scopus 로고
    • On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness
    • Desvillettes L., and Villani C. On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness. Comm. Partial Differential Equations 25 1-2 (2000) 179-259
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.1-2 , pp. 179-259
    • Desvillettes, L.1    Villani, C.2
  • 10
    • 0000278899 scopus 로고    scopus 로고
    • On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications
    • Desvillettes L., and Villani C. On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications. Comm. Partial Differential Equations 25 1-2 (2000) 261-298
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.1-2 , pp. 261-298
    • Desvillettes, L.1    Villani, C.2
  • 11
    • 0035526707 scopus 로고    scopus 로고
    • On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation
    • Desvillettes L., and Villani C. On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation. Comm. Pure Appl. Math. 54 1 (2001) 1-42
    • (2001) Comm. Pure Appl. Math. , vol.54 , Issue.1 , pp. 1-42
    • Desvillettes, L.1    Villani, C.2
  • 12
    • 1642284756 scopus 로고    scopus 로고
    • Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff
    • Desvillettes L., and Wennberg B. Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff. Comm. Partial Differential Equations 29 1-2 (2004) 133-155
    • (2004) Comm. Partial Differential Equations , vol.29 , Issue.1-2 , pp. 133-155
    • Desvillettes, L.1    Wennberg, B.2
  • 13
    • 0036882740 scopus 로고    scopus 로고
    • The Landau equation in a periodic box
    • Guo Y. The Landau equation in a periodic box. Comm. Math. Phys. 231 3 (2002) 391-434
    • (2002) Comm. Math. Phys. , vol.231 , Issue.3 , pp. 391-434
    • Guo, Y.1
  • 15
    • 67349194487 scopus 로고    scopus 로고
    • Regularity of entropy solutions for spatially homogeneous Boltzmann equation without angular cutoff
    • Huo Z.H., Morimoto Y., Ukai S., and Yang T. Regularity of entropy solutions for spatially homogeneous Boltzmann equation without angular cutoff. Kinetic Related Models 1 3 (2008) 453-489
    • (2008) Kinetic Related Models , vol.1 , Issue.3 , pp. 453-489
    • Huo, Z.H.1    Morimoto, Y.2    Ukai, S.3    Yang, T.4
  • 16
    • 35348971478 scopus 로고    scopus 로고
    • Hypoellipticity for a class of kinetic equations
    • Morimoto Y., and Xu C.-J. Hypoellipticity for a class of kinetic equations. J. Math. Kyoto Univ. 47 (2007) 129-152
    • (2007) J. Math. Kyoto Univ. , vol.47 , pp. 129-152
    • Morimoto, Y.1    Xu, C.-J.2
  • 17
    • 67349239513 scopus 로고    scopus 로고
    • Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
    • Morimoto Y., Ukai S., Xu C.-J., and Yang T. Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff. Discrete Contin. Dyn. Syst. Ser. A 24 1 (2009) 187-212
    • (2009) Discrete Contin. Dyn. Syst. Ser. A , vol.24 , Issue.1 , pp. 187-212
    • Morimoto, Y.1    Ukai, S.2    Xu, C.-J.3    Yang, T.4
  • 18
    • 0003244114 scopus 로고
    • 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 (1984) 141-156
    • (1984) Japan J. Appl. Math. , vol.1 , Issue.1 , pp. 141-156
    • Ukai, S.1
  • 19
    • 0032341369 scopus 로고    scopus 로고
    • On the spatially homogeneous Landau equation for Maxwellian molecules
    • Villani C. On the spatially homogeneous Landau equation for Maxwellian molecules. Math. Models Methods Appl. Sci. 8 (1998) 957-983
    • (1998) Math. Models Methods Appl. Sci. , vol.8 , pp. 957-983
    • Villani, C.1
  • 20
    • 0032338727 scopus 로고    scopus 로고
    • 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. Ration. Mech. Anal. 143 (1998) 273-307
    • (1998) Arch. Ration. Mech. Anal. , vol.143 , pp. 273-307
    • Villani, C.1
  • 21
    • 0038413035 scopus 로고    scopus 로고
    • A review of mathematical topics in collisional kinetic theory
    • Friedlander S., and Serre D. (Eds), North-Holland, Amsterdam
    • Villani C. A review of mathematical topics in collisional kinetic theory. In: Friedlander S., and Serre D. (Eds). Handbook of Fluid Mechanics (2002), North-Holland, Amsterdam
    • (2002) Handbook of Fluid Mechanics
    • Villani, C.1


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