instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
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The Muskat equation with data in the critical Sobolev space.
Conversaciones Fluidas
The Muskat problem is a nonlinear and nonlocal equation that modelises the dynamic of two fluids of different characteristics. In this talk, I shall present a global existence result for the Muskat problem with data in H^3/2. The proof is based on a new formulation of the Muskat problem. This formulation allows one to take advantage of (the hidden) oscillatory nature of this equation, which besides, allows one to use Besov space techniques to conclude the a priori estimates.
 
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