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18 papers · 2 filters
Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions
Carlos E. Kenig, Frank Merle
We show that if a solution of the defocusing cubic NLS in 3d remains bounded in the homogeneous Sobolev norm of order 1/2 in its maximal interval of existence, then the interval is…
A maximum principle for the Muskat problem for fluids with different densities
Diego Cordoba, Francisco Gancedo
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids…
On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations
Dongho Chae
We prove new \emph{a priori} estimates for the 3D Euler, the 3D Navier-Stokes and the 2D quasi-geostrophic equations by the method of similarity transforms.
A free-boundary problem for the evolution -Laplacian equation with a combustion boundary condition
Tung To
We study the existence, uniqueness and regularity of solutions of the equation under over-determined boundary conditions and $|Df…
On a question of Landis and Oleinik
Tu Nguyen
We answer in the affirmative a question posed by Landis and Oleinik on unique continuation of variable coefficients parabolic equations.
Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions
Carlos E. Kenig, David Preiss, Tatiana Toro
In this work we introduce the use of powerful tools from geometric measure theory (GMT) to study problems related to the size and structure of sets of mutual absolute continuity fo…