On the growth of high Sobolev norms for certain one-dimensional Hamiltonian PDEs
On the growth of high Sobolev norms for certain one-dimensional Hamiltonian PDEs
This paper is devoted to the study of large time bounds for the Sobolev norms of the solutions of the following fractional cubic Schrodinger equation on the torus : $$i \partial_t u = |D|^\alpha u+|u|^2 u, \quad u(0, \cdot)=u_0,$$ where $\alpha$ is a real parameter. We show that, apart from …