Uniqueness and continuous dependence of weak solutions in compressible magnetohydrodynamics

  • David Hoff
  • Eugene Tsyganov
Original Paper


We prove uniqueness and continuous dependence on initial data of weak solutions of the equations of compressible magnetohydrodynamics. The solutions we consider may exhibit discontinuities in density and in the gradients of velocity, temperature, and magnetic field. Continuous dependence is deduced by duality from existence and regularity of solutions of the adjoint of the first variation system. The analysis is complicated by the absence of strict parabolicity, the strong nonlinear coupling in the highest-order terms, and the lack of regularity in the coefficients of the adjoint system.

Mathematics Subject Classification (2000).

35A05 35M10 76N10 76W05 


Magnetohydrodynamics continuous dependence weak solutions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • David Hoff
    • 1
  • Eugene Tsyganov
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Max Planck Institute for Mathematics in the ScienceLeipzigGermany

Personalised recommendations