Abstract
We consider the Cauchy problem for the $L^2$-critical nonlinear Schrodinger equation with a nonlinear damping. According to the power of the damping term, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$.
Highlights
We study the blowup and the global existence of solutions for the focusing NLS equation with a nonlinear damping (N LSap): iut 4 d u
In [6], Darwich has proved in case of the linear damping (p = 0), the global existence in H1 for u0 L2 ≤ Q L2, and has showed that the log-log regime is stable by such perturbations
To prove this lemma, we shall need the following one:
Summary
On the L2-critical nonlinear Schrödinger Equation with a nonlinear damping.. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. ON THE L2-CRITICAL NONLINEAR SCHRO DINGER EQUATION WITH A NONLINEAR DAMPING
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