On the growth of Sobolev norms of solutions of the fractional defocusing NLS equation on the circle

DOI10.1016/j.anihpc.2016.02.002zbMath1370.37133OpenAlexW2316906444MaRDI QIDQ511515

Joseph Thirouin

Publication date: 21 February 2017

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2016.02.002

zbMATH Keywords

nonlinear wave equationHamiltonian systemfractional nonlinear Schrödinger equation

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Traveling wave solutions (35C07) Fractional partial differential equations (35R11)

Related Items (13)

On the growth of Sobolev norms for NLS on 2- and 3-dimensional manifolds ⋮ A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line ⋮ Quadratic fractional solitons ⋮ Wave Turbulence and Complete Integrability ⋮ Gibbs Measure Dynamics for the Fractional NLS ⋮ About the Quadratic Szegö Hierarchy ⋮ Refined probabilistic global well-posedness for the weakly dispersive NLS ⋮ Optimal bounds for the growth of Sobolev norms of solutions of a quadratic Szegő equation ⋮ Smoothing for the fractional Schroedinger equation on the torus and the real line ⋮ On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schrödinger equations ⋮ Global dynamics of small solutions to the modified fractional Korteweg-de Vries and fractional cubic nonlinear Schrödinger equations ⋮ Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations ⋮ Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

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