A combination of energy method and spectral analysis for study of equations of gas motion

Frontiers of Mathematics in China

Volumn 4, Issue 2, 2009, Pages 253-282

  Duan, Renjun ^a   Ukai, Seiji ^b   Yang, Tong ^b  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Asymptotic stability; Energy method; Linearization; Optimal rate; Spectral analysis

Indexed keywords

EID: 63849275800     PISSN: 16733452     EISSN: 16733576     Source Type: Journal    
DOI: 10.1007/s11464-009-0020-x     Document Type: Article

References (35)

1. K. Deckelnick 1992 Decay estimates for the compressible Navier-Stokes equations in unbounded domains Math Z 209 115 130
2. 2-decay for the compressible Navier-Stokes equations in unbounded domains Comm Partial Differential Equations 18 1445 1476
3. L. Desvillettes C. Villani 2005 On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation Invent Math 159 2 245 316
4. n Methods and Applications of Analysis 14 3 227 250
5. N ) Journal of Differential Equations 244 3204 3234
6. Duan R-J. Some Mathematical Theories on the Gas Motion under the Influence of External Forcing. Ph D Thesis. Hong Kong: City University of Hong Kong, 2008
7. q convergence rates for the Navier-Stokes equations with potential force Journal of Differential Equations 238 220 233
8. R.-J. Duan S. Ukai T. Yang H.-J. Zhao 2008 Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications Comm Math Phys 277 189 236
9. R.-J. Duan T. Yang C.-J. Zhu 2007 Navier-Stokes equations with degenerate viscosity, vacuum and gravitational force Mathematical Methods in the Applied Sciences 30 347 374
10. Y. Guo 2004 The Boltzmann equation in the whole space Indiana Univ Math J 53 1081 1094
11. Y. Guo 2006 Boltzmann diffusive limit beyond the Navier-Stokes approximation Comm Pure Appl Math 59 626 687
12. D. Hoff K. Zumbrun 1997 Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves Z angew Math Phys 48 597 614
13. Kawashima S. Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics. Thesis. Kyoto: Kyoto University, 1983
14. 3 J Differential Equations 184 587 619
15. 3 Commun Math Phys 200 621 659
16. Ladyzhenskaya O A. The Mathematical Theory of Viscous Incompressible Flow. 2nd English Ed (revised and enlarged). New York-London-Paris: Science Publishers, 1969, 1-224
17. T.-P. Liu W.-K. Wang 1998 The pointwise estimates of diffusion waves for the Navier-Stokes equations in odd multi-dimensions Commun Math Phys 196 145 173
18. T.-P. Liu T. Yang S.-H. Yu 2004 Energy method for the Boltzmann equation Physica D 188 3-4 178 192
19. T.-P. Liu S.-H. Yu 2004 Boltzmann equation: Micro-macro decompositions and positivity of shock profiles Commun Math Phys 246 1 133 179
20. T.-P. Liu S.-H. Yu 2008 Diffusion under gravitational and boundary effects Bull Inst Math Acad Sin (N S) 3 167 210
21. A. Matsumura T. Nishida 1980 The initial value problems for the equations of motion of viscous and heat-conductive gases J Math Kyoto Univ 20 67 104
22. A. Matsumura N. Yamagata 2001 Global weak solutions of the Navier-Stokes equations for multidimensional compressible flow subject to large external potential forces Osaka J Math 38 2 399 418
23. T. Nishida K. Imai 1976 Global solutions to the initial value problem for the nonlinear Boltzmann equation Publ Res Inst Math Sci 12 229 239
24. G. Ponce 1985 Global existence of small solutions to a class of nonlinear evolution equations Nonlinear Anal 9 339 418
25. Y. Shibata K. Tanaka 2007 Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid Comput Math Appl 53 605 623
26. Y. Shizuta 1983 On the classical solutions of the Boltzmann equation Commun Pure Appl Math 36 705 754
27. R. M. Strain 2006 The Vlasov-Maxwell-Boltzmann system in the whole space Commun Math Phys 268 2 543 567
28. R. M. Strain Y. Guo 2006 Almost exponential decay near Maxwellian Communications in Partial Differential Equations 31 417 429
29. S. Ukai 1974 On the existence of global solutions of mixed problem for non-linear Boltzmann equation Proceedings of the Japan Academy 50 179 184
30. S. Ukai 1976 Les solutions globales de l''equation de Boltzmann dans l'espace tout entier et dans le demi-espace C R Acad Sci Paris 282A 6 317 320
31. ∞ : Global and timeperiodic solutions Analysis and Applications 4 263 310
32. S. Ukai T. Yang H.-J. Zhao 2005 Global solutions to the Boltzmann equation with external forces Analysis and Applications 3 2 157 193
33. S. Ukai T. Yang H.-J. Zhao 2006 Convergence rate for the compressible Navier-Stokes equations with external force J Hyperbolic Diff Equations 3 561 574
34. S. Ukai T. Yang H.-J. Zhao 2006 Convergence rate to stationary solutions for Boltzmann equation with external force Chinese Ann Math 27 363 378
35. T. Yang H.-J. Zhao 2006 A new energy method for the Boltzmann equation Journal of Mathematical Physics 47 053301