数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (6): 1556-1572.doi: 10.1016/S0252-9602(10)60003-3

• 论文 • 上一篇    下一篇

ON GREEN'S FUNCTION FOR HYPERBOLIC-PARABOLIC SYSTEMS

 Tai-Ping Liu, Yanni Zeng   

  1. Department of Mathematics, Stanford University, Stanford, CA 94305, USA； Department of Mathematics, |University of Alabama at Birmingham, Birmingham, AL 35294, USA
  • 收稿日期:2009-10-25 出版日期:2009-11-20 发布日期:2009-11-20
  • 基金资助:

    The research of the first author was partially supported by NSC Grant 96-2628-M-001-011 and NSF Grant DMS-0709248. The research of the second author was partially supported by NSF Grant DMS-0207154.

ON GREEN'S FUNCTION FOR HYPERBOLIC-PARABOLIC SYSTEMS

 Tai-Ping Liu, Yanni Zeng   

  • Received:2009-10-25 Online:2009-11-20 Published:2009-11-20
  • Supported by:

    The research of the first author was partially supported by NSC Grant 96-2628-M-001-011 and NSF Grant DMS-0709248. The research of the second author was partially supported by NSF Grant DMS-0207154.

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摘要：

We study the Green's function for a general hyperbolic-parabolic system, including the Navier-Stokes equations for compressible fluids and the equations for magnetohydrodynamics. More generally, we consider general systems under the basic Kawashima-Shizuta type of
conditions. The first result is to make precise the secondary waves with subscale structure, revealing the nature of coupling of waves
pertaining to different characteristic families. The second result is on the continuous differentiability of the Green's function with
respect to a small parameter when the coefficients of the system are smooth functions of that parameter. The results significantly improve previous results obtained by the authors.

关键词: Greens functions, hyperbolic-parabolic systems, conservation laws, Navier-Stokes equations for compressible fluids

Abstract:

We study the Green's function for a general hyperbolic-parabolic system, including the Navier-Stokes equations for compressible fluids and the equations for magnetohydrodynamics. More generally, we consider general systems under the basic Kawashima-Shizuta type of
conditions. The first result is to make precise the secondary waves with subscale structure, revealing the nature of coupling of waves
pertaining to different characteristic families. The second result is on the continuous differentiability of the Green's function with
respect to a small parameter when the coefficients of the system are smooth functions of that parameter. The results significantly improve previous results obtained by the authors.

Key words: Greens functions, hyperbolic-parabolic systems, conservation laws, Navier-Stokes equations for compressible fluids

中图分类号: 

  • 35E05
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