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We introduce a set of coupled equations for multilayer water waves that removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the presence of shear. The new well-posed equations ...
Improved Local Well Posedness For Quasilinear Wave Equations In Dimension Three
Quasilinear Wave Equations Local Well Posedness
2014/4/3
This paper, in collaboration with I. Rodnianski, improves Tataru's well known recent regularity result for quasilinear wave equations. The paper relies on a significant improvement of the geometric te...
Bilinear Estimates And Applications To Nonlinear Wave Equations
Bilinear Estimates Applications Nonlinear Wave Equations
2014/4/3
This is a survey paper in collaboration with S. Selberg concerning optimal well posedness results for nonlinear wave equations such as Wave Maps, Maxwell-Klein-Gordon and Yang Mills. The survey provid...
A Commuting Vectorfield Approach To Strichartz Type Inequalities And Applications To Quasilinear Wave Equations
Quasilinear Wave Equations Applications
2014/4/3
This paper marks my wholehearted return to quasilinear wave equations, after a detour of more than ten years. I show that one can recover some of the recent results of Chemin-Bahouri and Tataru by red...