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7 papers · 2 filters
A regularity criterion for the dissipative quasi-geostrophic equations
Hongjie Dong, Natasa Pavlovic
We establish a regularity criterion for weak solutions of the dissipative quasi-geostrophic equations in mixed time-space Besov spaces.
Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity
Alexis Vasseur
In this short note, we give a link between the regularity of the solution to the 3D Navier-Stokes equation, and the behavior of the direction of the velocity . It is sho…
Symmetry and Asymmetry: The Method of Moving Spheres
Qinian Jin, Yanyan Li, Haoyuan Xu
We consider some nonlinear elliptic equations on and . By the method of moving spheres, we obtain the symmetry properties of solutions and some nonex…
Random homogenization of an obstacle problem
Luis A. Caffarelli, Antoine Mellet
We study the homogenization of an obstacle problem in a perforated domain. The holes are periodically distributed but have random size and shape. The capacity of the holes is assum…
A counterexample to regularity for parabolic fully nonlinear equations
Luis A. Caffarelli, Ulisse Stefanelli
We address the self-similar solvability of a singular parabolic problem and show that solutions to parabolic fully nonlinear equations are not expected to be .
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation
I. M. Gamba, V. Panferov, C. Villani
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution,…