# On the growth of Sobolev norms for the cubic Szegő equation

@inproceedings{Grard2014OnTG,
title={On the growth of Sobolev norms for the cubic Szegő equation},
author={Patrick G{\'e}rard and Sandrine Grellier},
year={2014}
}
• Published 2014
• Mathematics
The large time behavior of solutions to Hamiltonian partial differential equations is an important problem in mathematical physics. In the case of finite dimensional Hamiltonian systems, many features of the large time behavior of trajectories are described using the topology of the phase space. For a given infinite dimensional systems, several natural phase spaces, with different topologies, can be chosen, and the large time properties may strongly depend on the choice of such topologies. For…

### On certain Hamiltonian systems related to the cubic Szegő equation

The main purpose of this Ph.D. thesis is to study the long time behavior of solutionsto some Hamiltonian PDEs, i∂_t u=X_H (u), including global existence, growth of high Sobolev norms, scattering and

### Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation

• Mathematics
• 2010
We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes.

### Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation with a convolution potential

• Mathematics
• 2012
Fix $s>1$. Colliander, Keel, Staffilani, Tao and Takaoka proved in \cite{CollianderKSTT10} the existence of solutions of the cubic defocusing nonlinear Schr\"odinger equation in the two torus with

### Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds

• Mathematics
• 2004
We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any Riemannian compact manifold. As a consequence we infer low regularity local well-posedness

### An Inverse Problem for Self-adjoint Positive Hankel Operators

• Mathematics
• 2014
For a sequence {αn} 1=0 , we consider the Hankel operator �, realised as the infinite matrix in l 2 with the entries αn+m. We consider the subclass of such Hankel operators defined by the "double

### The cubic nonlinear Schr\"odinger equation in two dimensions with radial data

• Mathematics
• 2007
We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schr\"odinger equation $iu_t + \Delta u = \pm |u|^2 u$ for large spherically symmetric L^2_x(\R^2)

### On differential structures of polynomial spaces in control theory

• Mathematics
• 2012
A valuable number of works has been published about Hurwitz and Schur polynomials in order to known better their properties. For example it is known that the sets of Hurwitz and Schur polynomials are

### Integrals of Nonlinear Equations of Evolution and Solitary Waves

In Section 1 we present a general principle for associating nonlinear equations evolutions with linear operators so that the eigenvalues of the linear operator integrals of the nonlinear equation. A

### Operators, Functions, and Systems: An Easy Reading

Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 2: Model Operators and Systems, Mathematical Surveys and Monographs, Vol. 93, AMS,