This paper studies the Cauchy problem of the MHD equations with mass diffusion. We use the Tikhonov fixed point theorem to prove a local-in-time well-posedness theorem.
A problem with wells for the steady diffusion equation
β Scribed by Yu. M. Laevsky
- Book ID
- 111473916
- Publisher
- Pleiades Publishing
- Year
- 2010
- Tongue
- English
- Weight
- 617 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1995-4239
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider a mixed boundary problem for the Navier-Stokes equations in a bounded Lipschitz two-dimensional domain: we assign a Dirichlet condition on the curve portion of the boundary and a slip zero condition on its straight portion. We prove that the problem has a solution provided the boundary d
In this paper, we study the free-boundary problem associated with a singular diffusion equation. An entropy equality derived by the authors for BV solutions in an earlier paper is used in its formulation. Existence, uniqueness, and regularity results are obtained.