Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Gassot, P."'
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in $L^2(\mathbb{R})$ is obtained explicitly for generic rational initial data $u_0$. An explicit asymptotic wave profile $u^\mathr
Externí odkaz:
http://arxiv.org/abs/2410.17405
We show that the initial-value problem for the Benjamin-Ono equation on $\mathbb{R}$ with $L^2(\mathbb{R})$ rational initial data with only simple poles can be solved in closed form via a determinant formula involving contour integrals. The dimension
Externí odkaz:
http://arxiv.org/abs/2410.14870
A soliton ensemble is a particular kind of approximation of the solution of an initial-value problem for an integrable equation by a reflectionless potential that is well adapted to singular asymptotics like the small-dispersion limit. We study solit
Externí odkaz:
http://arxiv.org/abs/2311.05785
Autor:
Carles, Rémi, Gassot, Louise
We consider the mass-supercritical, defocusing, nonlinear Schr{\"o}dinger equation. We prove loss of regularity in arbitrarily short times for regularized initial data belonging to a dense set of any fixed Sobolev space for which the nonlinearity is
Externí odkaz:
http://arxiv.org/abs/2304.10958
Autor:
Gassot, Louise
We consider the zero-dispersion limit for the Benjamin-Ono equation on the torus for bell shaped initial data. Using the approximation by truncated Fourier series, we transform the eigenvalue equation for the Lax operator into a problem in the comple
Externí odkaz:
http://arxiv.org/abs/2301.03919
We obtain probabilistic local well-posedness in quasilinear regimes for the Schr\"odinger half-wave equation with a cubic nonlinearity. We need to use a refined ansatz because of the lack of probabilistic smoothing in the Picard's iterations, which i
Externí odkaz:
http://arxiv.org/abs/2209.14116
Autor:
Camps, Nicolas, Gassot, Louise
The purpose of this work is to evidence a pathological set of initial data for which the regularized solutions by convolution experience a norm-inflation mechanism, in arbitrarily short time. The result is in the spirit of the construction from Sun a
Externí odkaz:
http://arxiv.org/abs/2203.04840
Autor:
Gassot, Louise
We consider the zero-dispersion limit for the Benjamin-Ono equation on the torus. We prove that when the initial data is a single well, the zero-dispersion limit exists in the weak sense and is uniform on every compact time interval. Moreover, the li
Externí odkaz:
http://arxiv.org/abs/2111.06800
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:
Gassot, Louise
We consider the Benjamin-Ono equation on the torus with an additional damping term on the smallest Fourier modes (cos and sin). We first prove global well-posedness of this equation in $L^2_{r,0}(\mathbb{T})$. Then, we describe the weak limit points
Externí odkaz:
http://arxiv.org/abs/2010.05520