Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Bernier Joackim"'
Close to the origin, the nonlinear Klein--Gordon equations on the circle are nearly integrable Hamiltonian systems which have infinitely many almost conserved quantities called harmonic actions or super-actions. We prove that, at low regularity and w
Externí odkaz:
http://arxiv.org/abs/2406.12363
Autor:
Bernier, Joackim, Camps, Nicolas
We consider nonlinear Schr\"odinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of most of the
Externí odkaz:
http://arxiv.org/abs/2402.04122
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 63, Pp 78-108 (2018)
In [2], 1D×1D two-species Vlasov-Poisson simulations are performed by the semi-Lagrangian method. Thanks to a classical first order dispersion analysis, we are able to check the validity of their simulations; the extension to second order is perform
Externí odkaz:
https://doaj.org/article/dc826faa57ed45f688bfab8eae197c71
We prove an exponential stability result for the small solutions of the Schr{\"o}dinger-Poisson equation on the circle without exterior parameters in Gevrey class. More precisely we prove that for most of the initial data of Gevrey-norm smaller than
Externí odkaz:
http://arxiv.org/abs/2310.16476
In this paper, we succeed in integrating Strichartz estimates (encoding the dispersive effects of the equations) in Birkhoff normal form techniques. As a consequence, we deduce a result on the long time behavior of quintic NLS solutions on the circle
Externí odkaz:
http://arxiv.org/abs/2305.05236
We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex coefficients and are
Externí odkaz:
http://arxiv.org/abs/2303.10950
Autor:
Bernier, Joackim, Grébert, Benoît
We are interested in the long time behavior of solutions of the nonlinear Schr{\"o}dinger equation on the $d$-dimensional torus in low regularity, i.e. for small initial data in the Sobolev space $H^{s_0}(\mathbb T^d)$ with $s_0>d/2$. We prove that,
Externí odkaz:
http://arxiv.org/abs/2203.05799
Autor:
Alphonse, Paul, Bernier, Joackim
We characterize geometrically the semigroups generated by non-selfadjoint quadratic differential operators $(e^{-tq^w})_{t\geq 0}$ enjoying local smoothing effects and providing gains of integrability. More precisely, we prove that the evolution oper
Externí odkaz:
http://arxiv.org/abs/2111.11254
We describe the long time behavior of small non-smooth solutions to the nonlinear Klein-Gordon equations on the sphere S^2. More precisely, we prove that the low harmonic energies (also called super-actions) are almost preserved for times of order $\
Externí odkaz:
http://arxiv.org/abs/2109.02267
Autor:
Bernier, Joackim, Grébert, Benoît
We study the long time behavior of small solutions of semi-linear dispersive Hamiltonian partial differential equations on confined domains. Provided that the system enjoys a new non-resonance condition and a strong enough energy estimate, we prove t
Externí odkaz:
http://arxiv.org/abs/2102.09852