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Volumn 24, Issue 1, 2009, Pages 1-11

Littlewood-paley theory and regularity issues in Boltzmann homogeneous equations II. Non cutoff case and non Maxwellian molecules

Author keywords

Dimension theory; Multifractal analysis; Poincar ; Recurrences

Indexed keywords


EID: 67349205234     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2009.24.1     Document Type: Article
Times cited : (37)

References (21)
  • 1
    • 67449137912 scopus 로고    scopus 로고
    • Integral kernel estimates for a linear singular operator linked with Boltzmann equation
    • Indiana Univ. J. Maths, 55
    • R. Alexandra, Integral kernel estimates for a linear singular operator linked with Boltzmann equation. Part I: Small singularities 0 < ν > 1, Indiana Univ. J. Maths, 55 (2007), 1975-2021.
    • (2007) Part I: Small singularities 0 < ν > , vol.1 , pp. 1975-2021
    • Alexandra, R.1
  • 2
    • 67449158070 scopus 로고    scopus 로고
    • Lecture Notes. Given during C.H.K.E, Shanghai, Dec, In preparation, Version accessible through
    • R. Alexandre, Boltzmann equation and singular kernels, Lecture Notes. Given during C.H.K.E, Shanghai, Dec. 2006; In preparation, Version accessible through http://www.maths.univ-evry.fr/pages-perso/alexandre/index. html.
    • (2006) Boltzmann equation and singular kernels
    • Alexandre, R.1
  • 4
    • 18844411595 scopus 로고    scopus 로고
    • Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations. I. Non cutoff and Maxwell cases
    • R. Alexandre and M. ElSafadi, Littlewood-Paley decomposition and regularity issues in Boltzmann homogeneous equations. I. Non cutoff and Maxwell cases, Math. Meth. Models in Applied Sci., 15 (2005), 907-920.
    • (2005) Math. Meth. Models in Applied Sci , vol.15 , pp. 907-920
    • Alexandre, R.1    ElSafadi, M.2
  • 5
    • 67449137913 scopus 로고    scopus 로고
    • Integral kernel estimates for a linear singular operator linked with Boltzmann equation. Part II: High singularities 1 < ν < 2
    • Preprint
    • R. Alexandre and L. He, Integral kernel estimates for a linear singular operator linked with Boltzmann equation. Part II: High singularities 1 < ν < 2, Preprint.
    • Alexandre, R.1    He, L.2
  • 6
    • 67449122380 scopus 로고    scopus 로고
    • Regularization properties of non homogeneous kinetic equations and applications
    • Work in progress
    • R. Alexandre, Y. Morimoto, S. Ukai, C.-Y. Xu and T. Yang, Regularization properties of non homogeneous kinetic equations and applications, Work in progress.
    • Alexandre, R.1    Morimoto, Y.2    Ukai, S.3    Xu, C.-Y.4    Yang, T.5
  • 8
    • 67449127528 scopus 로고    scopus 로고
    • Smoothing effects for classical solutions of the full Landau equation
    • Preprint
    • Y. Chen, L. Desvillettes and L. He, Smoothing effects for classical solutions of the full Landau equation, Preprint, 2006.
    • (2006)
    • Chen, Y.1    Desvillettes, L.2    He, L.3
  • 9
    • 21844483733 scopus 로고
    • About the regularization properties of the non cut-off Kac equation
    • L. Desvillettes, About the regularization properties of the non cut-off Kac equation, Com. Math. Phys., 168 (1995), 417-440.
    • (1995) Com. Math. Phys , vol.168 , pp. 417-440
    • Desvillettes, L.1
  • 10
    • 0031495264 scopus 로고    scopus 로고
    • Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules
    • L. Desvillettes, Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules, Transport Theory Stat Phys., 26 (1997), 341-357.
    • (1997) Transport Theory Stat Phys , vol.26 , pp. 341-357
    • Desvillettes, L.1
  • 12
    • 33751053174 scopus 로고    scopus 로고
    • Stability and Uniqueness for the spatially homogeneous Boltz-mann equation with long-range interactions
    • To appear in
    • L. Desvillettes and C. Mouhot, Stability and Uniqueness for the spatially homogeneous Boltz-mann equation with long-range interactions, To appear in Arch. Rat. Mech. Analysis.
    • Arch. Rat. Mech. Analysis
    • Desvillettes, L.1    Mouhot, C.2
  • 13
    • 0000278898 scopus 로고    scopus 로고
    • On the spatially homogeneous Landau equation for hards potentials. Parti: Existence, uniqueness and smoothness
    • L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hards potentials. Parti: Existence, uniqueness and smoothness, Comm. P.D.E, 25 (2000), 179-259.
    • (2000) Comm. P.D.E , vol.25 , pp. 179-259
    • Desvillettes, L.1    Villani, C.2
  • 14
    • 1642284756 scopus 로고    scopus 로고
    • Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff
    • L. Desvillettes and B. Wennberg, Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff, Comm. P.D.E, 29 (2004), 133-155.
    • (2004) Comm. P.D.E , vol.29 , pp. 133-155
    • Desvillettes, L.1    Wennberg, B.2
  • 15
    • 67449115668 scopus 로고    scopus 로고
    • Smoothness of weak solutions of the spatially homogeneous Landau equation
    • M. El Safadi, Smoothness of weak solutions of the spatially homogeneous Landau equation, Analysis and Applications, 5 (2007), 29-49.
    • (2007) Analysis and Applications , vol.5 , pp. 29-49
    • El Safadi, M.1
  • 16
    • 67449167471 scopus 로고    scopus 로고
    • Gevrey regularity for Boltzmann homogeneous equation for maxwellian molecules
    • Preprint
    • Y. Morimoto, S. Ukai, C.-J. Xu and T. Yang, Gevrey regularity for Boltzmann homogeneous equation for maxwellian molecules, Preprint.
    • Morimoto, Y.1    Ukai, S.2    Xu, C.-J.3    Yang, T.4
  • 17
    • 67449137911 scopus 로고    scopus 로고
    • On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity
    • Preprint
    • C. Mouhot and N. Fournier, On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity, Preprint.
    • Mouhot, C.1    Fournier, N.2
  • 18
    • 4344621115 scopus 로고    scopus 로고
    • Regularity theory for the homogeneous Boltzmann equation with angular cuttof
    • C. Mouhot and C. Villani, Regularity theory for the homogeneous Boltzmann equation with angular cuttof, Arch. Rational Mech. Anal., 173 (2004), 169-212.
    • (2004) Arch. Rational Mech. Anal , vol.173 , pp. 169-212
    • Mouhot, C.1    Villani, C.2
  • 21
    • 0038413035 scopus 로고    scopus 로고
    • A Review of Mathematical Topics in Collisional Kinetic Theory
    • Ed. S. Friedlander, D. Serre
    • C. Villani, "A Review of Mathematical Topics in Collisional Kinetic Theory," Handbook of Fluid Mechanics, Ed. S. Friedlander, D. Serre, 2002.
    • (2002) Handbook of Fluid Mechanics
    • Villani, C.1


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