On the continuous resonant equation for NLS: II. Statistical study [PDF]
, 2015 We consider the continuous resonant (CR) system of the 2D cubic nonlinear Schr{\"o}dinger (NLS) equation. This system arises in numerous instances as an effective equation for the long-time dynamics of NLS in confined regimes (e.g. on a compact domain or
Germain, Pierre +2 more
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Low regularity well-posedness of KP-I equations: the three-dimensional case [PDF]
, 2022 In this paper, low regularity local well-posedness results for the Kadomtsev–Petviashvili–I equation posed in spatial dimension $d=3$ are proved. Periodic, non-periodic and mixed settings as well as generalized dispersion relations are considered. In the
Herr, Sebastian +2 more
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Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications [PDF]
, 2012 In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit.
Chekroun, Micka ël D. +1 more
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Nonlinear Schrödinger equation on four-dimensional compact manifolds [PDF]
, 2009 International ...
Gérard, Patrick, Pierfelice, Vittoria
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Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear Schr\"Odinger Equations [PDF]
, 2005 We study nonlinear Schr\"odinger equations, posed on a three dimensional Riemannian manifold $M$. We prove global existence of strong $H^1$ solutions on $M=S^3$ and $M=S^2\times S^1$ as far as the nonlinearity is defocusing and sub-quintic and thus we ...
Burq, N., Gerard, P., Tzvetkov, N.
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Random data Cauchy theory for supercritical wave equations II : A global existence result
, 2007 We prove that the subquartic wave equation on the three dimensional ball $\Theta$, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in $\cap_ ...
J. Bourgain +9 more
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Energy scattering for 2D critical wave equation
, 2008 We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the
Ibrahim, Slim +3 more
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Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3
, 2013 Consider a bilinear interaction between two linear dispersive waves with a generic resonant structure (roughly speaking, space and time resonant sets intersect transversally).
Bernicot, Frederic, Germain, Pierre
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Nonlinear Waves and Dispersive Equations [PDF]
, 2013 Nonlinear dispersive equations are models for nonlinear waves in a wide range of physical contexts. Mathematically they display an interplay between linear dispersion and nonlinear interactions, which can result in a wide range of outcomes from finite ...
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Almost sure well-posedness of the cubic nonlinear Schr\"odinger equation below L^2(T) [PDF]
, 2011 We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear Schr\"odinger equation (NLS) with initial data below L^2. In particular, we exhibit nonlinear smoothing when the initial data are randomized.
Colliander, James, Oh, Tadahiro
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