4 papers
Unified theory for regularity persistence of vortex patch boundaries
Marc Magaña
We establish a unified local theory for the persistence of Sobolev regularity of vortex patch boundaries in a family of two-dimensional active scalar equations with radial convolut…
The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations
Marc Magaña, Joan Mateu, Joan Orobitg
We prove the persistence of boundary smoothness of vortex patches for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations generalize the Euler equations by inc…
Sharp Strong Convergence in Ideal Flows
Haroune Houamed, Marc Magaña
We investigate the strong convergence of weak solutions to the two-dimensional Quasi-Geostrophic Shallow-Water (QGSW) equation as the inverse Rossby radius tends to zero. In this l…
Continuity of the solution map of some active scalar equations in Hölder and Zygmund spaces
Marc Magaña
We prove that the solution map for a family of non-linear transport equations in , with a velocity field given by the convolution of the density with a kernel that is…