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24 papers · 2 filters
Almost sure scattering for the one dimensional nonlinear Schrödinger equation
Nicolas Burq, Laurent Thomann
We consider the one-dimensional nonlinear Schrödinger equation with a nonlinearity of degree . We exhibit measures on the space of initial data for which we describe the non t…
Boundary value problems and Hardy spaces for elliptic systems with block structure
Pascal Auscher, Moritz Egert
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posednes…
Global dynamics of small solutions to the modified fractional Korteweg-de Vries and nonlinear Schrödinger equations
Jean-Claude Saut, Yuexun Wang
This paper concerns the modified fractional Korteweg-de Vries (modified fKdV) and nonlinear Schrödinger (modified fNLS) equations, with the dispersions |D|^α\partial_x and |D|^{α+1…
Long time behavior of solutions for a damped Benjamin-Ono equation
Louise Gassot
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 equatio…
Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system
Léo Girardin, Danielle Hilhorst
The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reactio…
Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition
Nicolas Burq, Chenmin Sun
We study in this article decay rates for Kelvin-Voigt damped wave equations under a geometric control condition. We prove that when the damping coefficient is sufficiently smooth (…