Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations
| Autor: | Haewon Yoon, Younghun Hong, Soonsik Kwon |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Applied Mathematics
General Mathematics Operator (physics) 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Fermion 01 natural sciences Stability (probability) Schrödinger equation Nonlinear system symbols.namesake Mathematics - Analysis of PDEs Dimension (vector space) 0103 physical sciences FOS: Mathematics symbols 010307 mathematical physics 0101 mathematics Element (category theory) Wave function Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Journal de Mathématiques Pures et Appliquées. 125:283-320 |
| ISSN: | 0021-7824 |
| DOI: | 10.1016/j.matpur.2018.12.003 |
| Popis: | We construct an extremizer for the Lieb–Thirring energy inequality (except the endpoint cases) developing the concentration-compactness technique for operator valued inequality in the formulation of the profile decomposition. Moreover, we investigate the properties of the extremizer, such as the system of Euler–Lagrange equations, regularity and summability. As an application, we study a dynamical consequence of a system of nonlinear Schrodinger equations with focusing cubic nonlinearities in three dimension when each wave function is restricted to be orthogonal. Using the critical element of the Lieb–Thirring inequality, we establish a global existence versus finite time blowup dichotomy. This result extends the single particle result of Holmer–Roudenko [35] to infinitely many particles system. |
| Databáze: | OpenAIRE |
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