142 citations · 1.3k across the 62 of their papers we have counts for
7 papers · 2 filters
Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise
Nathan E. Glatt-Holtz, Vlad C. Vicol
We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a very general non…
On the supercritically diffusive magneto-geostrophic equations
Susan Friedlander, Walter Rusin, Vlad Vicol
We address the well-posedness theory for the magento-geostrophic equation, namely an active scalar equation in which the divergence-free drift velocity is one derivative more singu…
Nonlinear maximum principles for dissipative linear nonlocal operators and applications
Peter Constantin, Vlad Vicol
We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide tran…
Global well-posedness for a slightly supercritical surface quasi-geostrophic equation
Michael Dabkowski, Alexander Kiselev, Vlad Vicol
We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velo…
On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations
Susan Friedlander, Vlad C. Vicol
We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the…
Holder continuity for a drift-diffusion equation with pressure
Luis Silvestre, Vlad Vicol
We address the persistence of Hölder continuity for weak solutions of the linear drift-diffusion equation with nonlocal pressure \[ u_t + b \cdot \grad u - \lap u = \grad p,\qquad…