数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 882-896.doi: 10.1016/S0252-9602(11)60283-X

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THE INVISCID AND NON-RESISTIVE LIMIT IN THE CAUCHY PROBLEM FOR 3-D NONHOMOGENEOUS INCOMPRESSIBLE MAGNETO-HYDRODYNAMICS

张剑文   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2009-07-10 修回日期:2010-02-20 出版日期:2011-05-20 发布日期:2011-05-20
  • 基金资助:

    This work was partly supported by NSFC (10801111;  10971171), the Natural Science Foundation of Fujian Province of China (2010J05011), and the Fundamental Research Funds for the Central Universities (2010121006).

THE INVISCID AND NON-RESISTIVE LIMIT IN THE CAUCHY PROBLEM FOR 3-D NONHOMOGENEOUS INCOMPRESSIBLE MAGNETO-HYDRODYNAMICS

 ZHANG Jian-Wen   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2009-07-10 Revised:2010-02-20 Online:2011-05-20 Published:2011-05-20
  • Supported by:

    This work was partly supported by NSFC (10801111;  10971171), the Natural Science Foundation of Fujian Province of China (2010J05011), and the Fundamental Research Funds for the Central Universities (2010121006).

摘要:

In this paper, the inviscid and non-resistive limit is justified for the local-in-time solutions to the equations of nonhomogeneous incompressible magneto-hydrodynamics (MHD) in R3. We prove that as the viscosity and resistivity go to zero, the solution of the Cauchy problem for the nonhomogeneous incompressible MHD system converges to the solution of the ideal MHD system. The  convergence rate is also obtained simultaneously.

关键词: 3-D nonhomogeneous incompressible MHD, ideal MHD, inviscid and non-resistive limit, local-in-time solution, convergence rate

Abstract:

In this paper, the inviscid and non-resistive limit is justified for the local-in-time solutions to the equations of nonhomogeneous incompressible magneto-hydrodynamics (MHD) in R3. We prove that as the viscosity and resistivity go to zero, the solution of the Cauchy problem for the nonhomogeneous incompressible MHD system converges to the solution of the ideal MHD system. The  convergence rate is also obtained simultaneously.

Key words: 3-D nonhomogeneous incompressible MHD, ideal MHD, inviscid and non-resistive limit, local-in-time solution, convergence rate

中图分类号: 

  • 76W05