Some estimates of solutions for the equations of motion of compressible viscous fluid in the three-dimensional exterior domain

Journal of Differential Equations

Volumn 184, Issue 2, 2002, Pages 587-619

  Kobayashi, Takayuki ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Analytic semigroup; Compressible viscous fluid; L1 estimates; Lq Lp estimates

Indexed keywords

EID: 0037144874     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2002.4158     Document Type: Article

References (16)

1. J. Bergh and J. Löfström, "Interpolation Spaces: an Introduction," Springer-Verlag, Berlin/Heidelberg/New York, 1976.
2. K. Deckelnick, Decay estimates for the compressible Navier-Stokes equations in unbounded domain, Math. Z. 209 (1992), 115-130.
3. 2-decay for the compressible Navier-Stokes equations in unbounded domains, Comm. Partial Differential Equations 18 (1993), 1445-1476.
4. D. Hoff and K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J. 44 (1995), 604-676.
5. D. Hoff and K. Zumbrun, Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves, Z. Angew. Math. Phys. 48 (1997), 597-614.
6. q spaces, Math. Ann. 285 (1989), 265-268.
7. H. Iwashita and Y. Shibata, On the analyticity of spectral functions for some exterior boundary value problem, Glas. Mat. Ser. III 23 (1988), 291-313.
8. 3, Tsukuba J. Math. 21 (1997), 629-670.
9. 3, Proc. Japan Acad. Ser. A 73 (1997), 126-129.
10. T. Kobayashi and Y. Shibata, On the Oseen equation in the exterior domains, Math. Ann. 310 (1998), 1-45.
11. 3, Comm. Math. Phys 200 (1999), 621-659.
12. T.-P. Liu and W. Wang, The pointwise estimates of diffusion wave for the Navier-Stokes system in odd multi-dimensions, Comm. Math. Phys. 196 (1998), 145-173.
13. A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A 55 (1979), 337-342.
14. A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids, Comm. Math. Phys. 89 (1983), 445-464.
15. G. Ponce, Global existence of small solutions to a class of nonlinear evolution equations, Nonlinear Anal. 9 (1985), 339-418.
16. Y. Shibata, On the global existence of classical solutions of second order fully nonlinear hyperbolic equations with first order dissipation in the exterior domain, Tsukuba J. Math. 7 (1983), 1-68.