De Vlad Vicol
Apparaît également dans la collection : ECM 2024 Plenary Speakers
We consider the 2D Muskat equation for the interface between two constant density fluids in an incompressible porous medium, with velocity given by Darcy's law. We establish that as long as the slope of the interface between the two fluids remains bounded and uniformly continuous, the solution remains regular. The proofs exploit the nonlocal nonlinear parabolic nature of the equations through a series of nonlinear lower bounds for nonlocal operators. These are used to deduce that as long as the slope of the interface remains uniformly bounded, the curvature remains bounded. We provide furthermore a global regularity result for small initial data: if the initial slope of the interface is sufficiently small, there exists a unique solution for all time. This is joint work with P. Constantin, F. Gancedo, and R. Shvydkoy.
De Patrick Gerard
De Hatem Zaag
De Thomas Kappeler
De Michal Kowalczyk
De Cécile Huneau
De Mihalis Dafermos
De Andrea Nahmod
De Benjamin Schlein
De Chris Sogge
De Alexandru Ionescu
De Vlad Vicol
De Thomas Alazard
De Robert Jerrard
De Camillo de Lellis
De Albert Schwarz
De Chao Li
De Albert Schwarz
De Albert Schwarz
De Stephen Coombes , Peter Liddle
De Victor Kleptsyn
De Albert Schwarz
