Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Latocca, Mickaël"'
Autor:
Burq, Nicolas, Latocca, Mickaël
We prove Strichartz estimates for a class of Baouendi--Grushin operators acting either on the Euclidean space or a product of the type $\mathbb{R}^{d_1} \times M$, where $(M,g)$ is a smooth compact manifold with no boundary. We then give an applicati
Externí odkaz:
http://arxiv.org/abs/2411.19808
We consider the Wick ordered cubic Schr\"odinger equation (NLS) posed on the two-dimensional sphere, with initial data distributed according to a Gaussian measure. We show that the second Picard iteration does not improve the regularity of the initia
Externí odkaz:
http://arxiv.org/abs/2404.18241
Autor:
Latocca, Mickaël, Munnier, Vincent
This paper establishes Carleson embeddings of M{\"u}ntz spaces $M^q_{\Lambda}$ into weighted Lebesgue spaces $L^p(\mathrm{d}\mu)$, where $\mu$ is a Borel regular measure on $[0,1]$ satisfying $\mu([1-\varepsilon])\lesssim \varepsilon^{\beta}$. In the
Externí odkaz:
http://arxiv.org/abs/2403.00395
Autor:
Bedrossian, Jacob, Latocca, Mickaël
In this article we consider the two-dimensional incompressible Euler equations and give a sufficient condition on Gaussian measures of jointly independent Fourier coefficients supported on $H^{\sigma}(\mathbb{T}^2)$ ($\sigma>3$) such that these measu
Externí odkaz:
http://arxiv.org/abs/2307.04214
We consider H\"older continuous weak solutions $u\in C^\gamma(\Omega)$, $u\cdot n|_{\partial \Omega}=0$, of the incompressible Euler equations on a bounded and simply connected domain $\Omega\subset\mathbb{R}^d$. If $\Omega$ is of class $C^{2,1}$ the
Externí odkaz:
http://arxiv.org/abs/2301.06482
Publikováno v:
Calc. Var. Partial Differ. Equ. 62 (2023), no. 3. Paper No. 85, 31 pp
We prove that the hydrodynamic pressure $p$ associated to the velocity $u\in C^\theta(\Omega)$, $\theta\in(0,1)$, of an inviscid incompressible fluid in a bounded and simply connected domain $\Omega\subset \mathbb R^d$ with $C^{2+}$ boundary satisfie
Externí odkaz:
http://arxiv.org/abs/2205.00929
Autor:
Latocca, Mickaël, Munnier, Vincent
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 March 2025 543(1)
Autor:
Gassot, Louise, Latocca, Mickaël
We study the local well-posedness of the nonlinear Schr\"odinger equation associated to the Grushin operator with random initial data. To the best of our knowledge, no well-posedness result is known in the Sobolev spaces $H^k$ when $k \leq \frac{3}{2
Externí odkaz:
http://arxiv.org/abs/2103.03560
Autor:
Latocca, Mickaël
We consider the radial nonlinear Schr\"odinger equation $i\partial_tu +\Delta u = |u|^{p-1}u$ in dimension $d\geqslant 2$ for $p\in \left(1,1+\frac{4}{d}\right]$ and construct a natural Gaussian measure $\mu_0$ which support is almost $L^2_{\text{rad
Externí odkaz:
http://arxiv.org/abs/2011.06309
Autor:
Latocca, Mickaël
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 spaces so that strong solutions are also known to exist. The proof follows
Externí odkaz:
http://arxiv.org/abs/2002.11086