Loss of regularity for supercritical nonlinear Schrödinger equations
✍ Scribed by Thomas Alazard; Rémi Carles
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 317 KB
- Volume
- 343
- Category
- Article
- ISSN
- 0025-5831
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📜 SIMILAR VOLUMES
In this paper we consider the regularity of solutions to nomlinear Schrödinger equations (NLS), \[ \begin{aligned} i \hat{C}, u+\frac{1}{3} \| u & =F(u, u) . & & (t, x) \in \mathbb{R} \times \mathbb{B}^{\prime \prime}, \\ u(0) & =\phi . & & x \in \mathbb{R}^{u} . \end{aligned} \] where \(F\) is a po
We prove that the global attractor for a weakly damped nonlinear Schr6dinger equation is smooth, i.e., it is made of smooth functions when the forcing term is smooth. Our study relies on a new approach that works for dispersive equations that are weakly dissipative, i.e., for equations for which the