Critical nonlinear Schrödinger equations in higher space dimensions
| Autor: | Pavel I. Naumkin, Nakao Hayashi, Chunhua Li |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
large time asymptotics
General Mathematics 010102 general mathematics 35B40 Absolute value (algebra) Space (mathematics) Lambda 01 natural sciences critical NLS equations Schrödinger equation 010101 applied mathematics 35Q55 symbols.namesake Uniform norm Fourier transform Bounded function symbols Initial value problem 0101 mathematics higher space dimensions Mathematics Mathematical physics |
| Zdroj: | J. Math. Soc. Japan 70, no. 4 (2018), 1475-1492 |
| Popis: | We study the critical nonlinear Schrodinger equations \[ i\partial _{t}u+\frac{1}{2}\Delta u = \lambda \vert u\vert^{{2}/{n}}u, \quad (t,x) \in \mathbb{R}^{+}\times \mathbb{R}^{n}, \] in space dimensions $n\geq 4$, where $\lambda \in \mathbb{R}$. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm. |
| Databáze: | OpenAIRE |
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