# MATHEMATICAL ANALYSIS OF TWO-FLUID PROBLEMS

# MATHEMATICAL ANALYSIS OF TWO-FLUID PROBLEMS

This chapter deals with the theoretical aspects of multifluid magnetohydrodynamics problems. In addition to the coupling between hydrodynamics and electromagnetics examined in Chapter 2, the high nonlinearity that now needs to be addressed is geometrical in nature. It results from the presence of one (or many) free interface(s) separating the fluids, assumed non-miscible. The mathematical analysis is substantially more intricate, and a long list of simple, however open, problems can be drawn up. Throughout the chapter, the equation that plays a crucial role is the equation of the conservation of mass. Owing to an argument based on the theory of renormalized solutions, a global-in-time existence result of weak solution is proved. The long-time behaviour of sufficiently regular solutions is also investigated.

*Keywords:*
multifluid flows, renormalized solutions, weak solutions, long-time behaviour, transport equation, energy inequalities, a priori estimates

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .