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of 162
pro vyhledávání: '"Thomann, Laurent"'
We study the Lowest Landau Level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we study well-posedness and establish the existence of stationary solutio
Externí odkaz:
http://arxiv.org/abs/2404.06085
The purpose of this article is to construct global solutions, in a probabilistic sense, for the nonlinear Schr{\"o}dinger equation posed on $\mathbb{R}^d$, in a supercritical regime. Firstly, we establish Bourgain type bilinear estimates for the harm
Externí odkaz:
http://arxiv.org/abs/2304.10979
The study is devoted to the interpretation and wellposedness of a stochastic NLS model with a quadratic nonlinearity and a space-time fractional noise. We focus on a rough regime corresponding to the case where the Hurst indexes of the fractional noi
Externí odkaz:
http://arxiv.org/abs/2304.03114
Autor:
Thomann, Laurent, Burq, Nicolas
Publikováno v:
RIMS Workshop: Nonlinear and Random Waves, RIMS, Oct 2022, Kyoto (Japan), France
In this note, we give an overview of some results obtained in [3]. This latter work is devoted to the study of the one-dimensional nonlinear Schr{\"o}dinger equation with random initial conditions. Namely, we describe the nonlinear evolution of Gauss
Externí odkaz:
http://arxiv.org/abs/2303.06964
Autor:
Thomann, Laurent
We consider a coupled system of nonlinear Lowest Landau Level equations. We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result. We also show a long time stability resu
Externí odkaz:
http://arxiv.org/abs/2111.05035
Autor:
Burq, Nicolas, Thomann, Laurent
We consider the one-dimensional nonlinear Schr\"odinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schr\"odinger flow and we show that t
Externí odkaz:
http://arxiv.org/abs/2012.13571
Autor:
Thomann, Laurent
We give an example of a linear, time-dependent, Schr{\"o}dinger operator with optimal growth of Sobolev norms. The construction is explicit, and relies on a comprehensive study of the linear Lowest Landau Level equation with a time-dependent potentia
Externí odkaz:
http://arxiv.org/abs/2006.02674
Autor:
Schwinte, Valentin, Thomann, Laurent
Publikováno v:
Pure Appl. Analysis 3 (2021) 189-222
We study coupled systems of nonlinear lowest Landau level equations, for which we prove global existence results with polynomial bounds on the possible growth of Sobolev norms of the solutions. We also exhibit explicit unbounded trajectories which sh
Externí odkaz:
http://arxiv.org/abs/2006.01468
We study a stochastic Schr{\"o}dinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension less than 3. When the Hurst index is large enough, we prove local well-posedness of the problem using classical
Externí odkaz:
http://arxiv.org/abs/2005.01370
Autor:
Chambrion, Thomas, Thomann, Laurent
In 1982, Ball, Marsden, and Slemrod proved an obstruction to the controllability of linear dynamics with a bounded bilinear control term. This note presents an example of nonlinear dynamics with respect to the state for which this obstruction still h
Externí odkaz:
http://arxiv.org/abs/1903.04185