Mickael Latocca

activity

20182026

most citedAlmost Sure Existence of Global Solutions for Supercritical Semilinear Wave Equations

9 citations · 20 across the 14 of their papers we have counts for

collaborators

16 papers

math.AP2026

Obstruction to quasi-invariance of Gaussian measures under transport flows on Riemannian Manifolds

Anne-Sophie de Suzzoni, Mickaël Latocca

We prove an obstruction to quasi-invariance of Gaussian fields under divergence free transport flows on Riemannian manifolds. For the centered Gaussian field with covariance $(1-Δ_…

math.AP2026

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 $ρ$ of solutions to the free Liouville equation on flat tori. In dimension one, we obtain the optimal range of estimates fo…

math.AP2025

Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation

Luigi De Rosa, Mickaël Latocca, Jaemin Park

For any initial datum $θ_{0} \in L_{x}^{\frac{4}{3}}$ it is proved the existence of a global-in-time weak solution $θ \in L_{t}^{\infty} L_{x}^{\frac{4}{3}}$ to the surface quasi-geostrophic equat…

math.FA2025

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 $- Δ + ∣ x ∣^{2}$ on $R^{d}$ with d \geq 2$$. More precisely we obtain a necessary…

math.AP2025

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…

math.FA2024

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 $L…

math.AP2024

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 $R^{d_{1}} \times M$ , where $(M, g)$ is…

math.AP2024★ 1 cited

The Second Picard iteration of NLS on the $2 d$ 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 s…

math.CA2024

Generalized Carleson Embeddings of M{ü}ntz Spaces

Mickaël Latocca, Vincent Munnier

This paper establishes Carleson embeddings of M{ü}ntz spaces $M_{Λ}^{q}$ into weighted Lebesgue spaces $L^{p} (d μ)$ , where $μ$ is a Borel regular measure on $[0, 1]$ satisfying $μ…

math.AP2023

Non-invariance of Gaussian Measures under the 2D Euler Flow

Jacob Bedrossian, Mickaël Latocca

In this article we consider the two-dimensional incompressible Euler equations and give a sufficient condition on Gaussian measures of jointly independent Fourier coefficients supp…

math.AP2023★ 4 cited

Full double Hölder regularity of the pressure in bounded domains

Luigi De Rosa, Mickaël Latocca, Giorgio Stefani

We consider Hölder continuous weak solutions $u \in C^{γ} (Ω)$ , $u \cdot n ∣_{\partial Ω} = 0$ , of the incompressible Euler equations on a bounded and simply connected domain $Ω\subset\mat…

math.AP2022★ 5 cited

On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains

Luigi De Rosa, Mickaël Latocca, Giorgio Stefani

We prove that the hydrodynamic pressure $p$ associated to the velocity $u \in C^{θ} (Ω)$ , $θ \in (0, 1)$ , of an inviscid incompressible fluid in a bounded and simply connected domain $Ω\s…

math.AP2021

Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian

Louise Gassot, Mickaël Latocca

We study the local well-posedness of the nonlinear Schrödinger equation associated to the Grushin operator with random initial data. To the best of our knowledge, no well-posedness…

math.AP2020★ 1 cited

Almost Sure Scattering at Mass Regularity for Radial Schrödinger Equations

Mickaël Latocca

We consider the radial nonlinear Schrödinger equation $i \partial_{t} u + Δ u = ∣ u ∣^{p - 1} u$ in dimension $d ⩾ 2$ for $p \in (1, 1 + \frac{4}{d}]$ and construct a natural Ga…

math.AP2020

Construction of High Regularity Invariant Measures for the 2D Euler Equations and Remarks on the Growth of the Solutions

Mickaël Latocca

We consider the Euler equations on the two-dimensional torus and construct invariant measures for the dynamics of these equations, concentrated on sufficiently regular Sobolev spac…

math.AP2018★ 9 cited

Almost Sure Existence of Global Solutions for Supercritical Semilinear Wave Equations

Mickaël Latocca

We prove that for almost every initial data $(u_{0}, u_{1}) \in H^{s} \times H^{s - 1}$ with $s > \frac{p - 3}{p - 1}$ there exists a global weak solution to the supercritical semilinear wave e…

Obstruction to quasi-invariance of Gaussian measures under transport flows on Riemannian Manifolds

Strichartz Estimates for the Liouville Equation on Euclidean Tori and Applications to Kakeya

Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation

Almost Sure Uniform Convergence Of Random Hermite Series

Well-Posedness of the Free Boundary Incompressible Porous Media Equation

Marcinkiewicz Type Theorems for Interpolation of Operators Acting on M{ü}ntz Spaces

Strichartz Estimates for a Class of Baouendi-Grushin Operators

The Second Picard iteration of NLS on the 2d sphere does not regularize Gaussian random initial data

Generalized Carleson Embeddings of M{ü}ntz Spaces

Non-invariance of Gaussian Measures under the 2D Euler Flow

Full double Hölder regularity of the pressure in bounded domains

On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains

Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian

Almost Sure Scattering at Mass Regularity for Radial Schrödinger Equations

Construction of High Regularity Invariant Measures for the 2D Euler Equations and Remarks on the Growth of the Solutions

Almost Sure Existence of Global Solutions for Supercritical Semilinear Wave Equations

The Second Picard iteration of NLS on the $2 d$ sphere does not regularize Gaussian random initial data