17 citations · 53 across the 7 of their papers we have counts for
7 papers
On the local existence for an active scalar equation in critical regularity setting
Walter Rusin, Fei Wang
In this note, we address the local well-posedness for the active scalar equation , where . The local existence of…
An anisotropic partial regularity criterion for the Navier-Stokes equations
I. Kukavica, W. Rusin, M. Ziane
In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier--Stokes equations. We prove an interior regularity criterion involving only…
The magneto-geostrophic equations: a survey
Susan Friedlander, Walter Rusin, Vlad Vicol
We discuss recent results obtained by the authors, regarding the analysis of the magneto-geostrophic equation: a model proposed by Moffat and Loper to study the geodynamo and turbu…
On the second iterate for active scalar equations
Susan Friedlander, Walter Rusin
We consider an iterative resolution scheme for a broad class of active scalar equations with a fractional power γof the Laplacian and focus our attention on the second iterate. The…
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…
Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations
Walter Rusin
We study the question weather weak solutions to a class of active scalar equations, with the drift velocity and the active scalar related via a Fourier multiplier of order zero, ar…