35 citations · 62 across the 14 of their papers we have counts for
18 papers
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…
Skeleton for the one-dimensional aggregation equation
Juan Carlos Cantero, Joan Orobitg
For the aggregation equation in , we consider the evolution of an initial density corresponding to the characteristic function of some set . We study the limit mea…
The regularity of the boundary of vortex patches for some non-linear transport equations
J. C. Cantero, J. Mateu, J. Orobitg +1
We prove the persistence of boundary smoothness of vortex patches for a non-linear transport equation in with velocity field given by convolution of the density with…
Distributional solutions of the Beltrami equation
A. L. Baisón, A. Clop, J. Orobitg
We study the distributional solutions to the (generalized) Beltrami equation under Sobolev assumptions on the Beltrami coefficients. In this setting, we prove that these distributi…
Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
Albert Clop, Heikki Jylhä, Joan Mateu +1
We prove well-posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field, but not on its divergence. As a…
Fractional differentiability for solutions of nonlinear elliptic equations
Antonio L. Baisón, Albert Clop, Raffaella Giova +2
We study nonlinear elliptic equations in divergence form When has linear growth in , and assumi…