Displaying similar documents to “A variational inequality for discontinuous solutions of degenerate parabolic equations.”

Existence of strong solutions for nonisothermal Korteweg system

Boris Haspot (2009)

Annales mathématiques Blaise Pascal

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This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model. We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical...

Geometric structure of magnetic walls

Myriam Lecumberry (2005)

Journées Équations aux dérivées partielles

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After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.

Some recent results on the Muskat problem

Angel Castro, Diego Córdoba, Francisco Gancedo (2010)

Journées Équations aux dérivées partielles

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We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.

On the global existence for the axisymmetric Euler equations

Hammadi Abidi, Taoufik Hmidi, Sahbi Keraani (2008)

Journées Équations aux dérivées partielles

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This paper deals with the global well-posedness of the 3 D axisymmetric Euler equations for initial data lying in critical Besov spaces B p , 1 1 + 3 p . In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity .