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6 papers · 2 filters
On the 2d Zakharov system with L^2 Schrödinger data
Ioan Bejenaru, Sebastian Herr, Justin Holmer +1
We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity…
Interface evolution: water waves in 2-D
Antonio Cordoba, Diego Cordoba, Francisco Gancedo
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, i…
Renormalization and blow up for the critical Yang-Mills problem
Joachim Krieger, Wilhelm Schlag, Daniel Tataru
We consider the Yangs-Mills equations in 4+1 dimensions. This is the energy critical case and we show that it admits a family of solutions which blow up in finite time. They are ob…
Interface evolution: the Hele-Shaw and Muskat problems
Antonio Cordoba, Diego Cordoba, Francisco Gancedo
We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from Darcy's law. The free boundary is given by the discontinui…
Convergence of nonlocal threshold dynamics approximations to front propagation
Luis A. Caffarelli, Panagiotis E. Souganidis
In this note we prove that appropriately scaled threshold dynamics-type algorithms corresponding to the fractional Laplacian of order converge to moving fronts. When $…
Regularity of the minimizers in the composite membrane problem in R^2
Sagun Chanillo, Carlos E. Kenig, Tung TO
We study the regularity of minimizers to the composite membrane problem in the plane (ie given a domain omega and a positive number A, smaller than the measure of omega, minimize t…