6 papers
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…
Almost Sure Uniform Convergence Of Random Hermite Series
Rafik Imekraz, Mickaël Latocca
We continue the analysis of random series associated to the multidimensional harmonic oscillator on with d \geq 2$$. More precisely we obtain a necessar…
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…
Marcinkiewicz Type Theorems for Interpolation of Operators Acting on M{ü}ntz Spaces
Mickaël Latocca, Vincent Munnier
We prove interpolation results in the spirit of the Marcinkiewicz theorem. The operators considered in this article are defined on Müntz spaces, which are not dense subspaces of $…
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…