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9 papers · 2 filters
A priori estimates for fluid Interface problems
Jalal Shatah, Chongchun Zeng
We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interfa…
Moment bounds for the Smoluchowski equation and their consequences
Alan Hammond, Fraydoun Rezakhanlou
We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities α(n,…
Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO^{-1}
Pierre Germain, Nataša Pavlović, Gigliola Staffilani
In 2001, H. Koch and D. Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in for initial data small enough in $…
An extension problem related to the fractional Laplacian
Luis Caffarelli, Luis Silvestre
The operator square root of the Laplacian $(-\lap)^{1/2}$ can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet bounda…
Geometry and a priori estimates for free boundary problems of the Euler's equation
Jalal Shatah, Chongchun Zeng
In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition…
Tug of war with noise: a game theoretic view of the p-Laplacian
Yuval Peres, Scott Sheffield
Fix a bounded domain Omega in R^d, a continuous function F on the boundary of Omega, and constants epsilon>0, p>1, and q>1 with p^{-1} + q^{-1} = 1. For each x in Omega, let u^epsi…