Scattering for the 3D Gross-Pitaevskii equation

Abstract

We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by Gérard \cite{Gerard}. In this paper we prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.

28 pages; Correct some mistakes, the main results remain the same

References in corpus (5)

• Travelling waves for the Gross-Pitaevskii equation II
• Decay estimates for a class of wave equations
• Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in ${\mathbb{R}}^{1+4}$
• Small energy scattering for the Zakharov system with radial symmetry

Cited by in corpus (9)

• On the low Mach number limit for Quantum Navier-Stokes equations
• Exactly solvable Gross-Pitaevskii type equations
• On the boundary Strichartz estimates for wave and Schrödinger equations
• The final-state problem for the cubic-quintic NLS with non-vanishing boundary conditions
• Scattering below the ground state for the 2D non-linear Schrödinger and Klein-Gordon equations revisited
• Scattering for the quadratic Klein-Gordon equations
• Small data scattering of the inhomogeneous cubic-quintic NLS in 2 dimensions
• Small data scattering of semirelativistic Hartree equation
• Wellposedness and scattering for the generalized Boussinesq equation