论文信息 - Small Data Scattering for the Nonlinear Schrödinger Equation on Product Spaces

Small Data Scattering for the Nonlinear Schrödinger Equation on Product Spaces

We consider the cubic nonlinear Schrödinger equation, posed on ℝ n × M, where M is a compact Riemannian manifold and n ≥ 2. We prove that under a suitable smallness in Sobolev spaces condition on the data there exists a unique global solution which scatters to a free solution for large times.

Nikolay Tzvetkov | N. Tzvetkov | N. Visciglia | Nicola Visciglia

[1] Paul H. Rabinowitz,et al. On a class of nonlinear Schrödinger equations , 1992 .

[2] Thierry Cazenave,et al. The Cauchy problem for the critical nonlinear Schro¨dinger equation in H s , 1990 .

[3] J. Ginibre,et al. On a class of nonlinear Schrödinger equations. II. Scattering theory, general case , 1979 .

[4] J. Bourgain,et al. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations , 1993 .

[5] Tohru Ozawa,et al. Long range scattering for nonlinear Schrödinger equations in one space dimension , 1991 .

[6] Y. Tsutsumi. L$^2$-Solutions for Nonlinear Schrodinger Equations and Nonlinear Groups , 1985 .

[7] H. Takaoka,et al. On 2D Nonlinear Schrödinger Equations with Data on R×T☆ , 2001 .

[8] J. Ginibre,et al. On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case , 1979 .

[9] P. Gérard,et al. Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds , 2004 .

[10] T. Cazenave. Semilinear Schrodinger Equations , 2003 .

[11] N. Tzvetkov,et al. Strichartz estimates for partially periodic solutions to Schr , 2010, 1011.0591.