5 papers · 1 filter
Strichartz Estimates for the Liouville Equation on Euclidean Tori and Applications to Kakeya
Pierre Germain, Mickaël Latocca
We prove Strichartz estimates for the space-time density of solutions to the free Liouville equation on flat tori. In dimension one, we obtain the optimal range of estimates f…
Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation
Luigi De Rosa, Mickaël Latocca, Jaemin Park
For any initial datum it is proved the existence of a global-in-time weak solution to the surface quasi-geostrophic equ…
Well-Posedness of the Free Boundary Incompressible Porous Media Equation
Mickaël Latocca, Huy Q. Nguyen
We consider the free boundary incompressible porous media equation which describes the dynamics of a density transported by a Darcy flow in the field of gravity, with a free bounda…
Strichartz Estimates for a Class of Baouendi-Grushin Operators
Nicolas Burq, Mickaël Latocca
We prove Strichartz estimates for a class of Baouendi--Grushin operators acting either on the Euclidean space or a product of the type , where is…
The Second Picard iteration of NLS on the sphere does not regularize Gaussian random initial data
Nicolas Burq, Nicolas Camps, Mickaël Latocca +2
We consider the Wick ordered cubic Schrödinger equation (NLS) posed on the two-dimensional sphere, with initial data distributed according to a Gaussian measure. We show that the…