Local well-posedness of nonlinear dispersive equations on modulation spaces

Abstract

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the NLS, NLW and NLKG equations with Cauchy data in modulation spaces $M{p,1}_{0,s}$.

11 pages

Cited by in corpus (9)

• Schrödinger equations with rough Hamiltonians
• On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p,q}(\mathbb{R})$
• Norm inflation for nonlinear Schrodinger equations in Fourier-Lebesgue and modulation spaces of negative regularity
• Nonlinear Schrödinger equation, differentiation by parts and modulation spaces
• NLS in the modulation space $M_{2,q}(\mathbb{R})$
• Time-frequency analysis of the Dirac equation
• Local well-posedness for the nonlinear Schrödinger equation in the intersection of modulation spaces $M_{p,q}^s({\mathbb{R}}^d)\cap M_{\infty ,1}({\mathbb{R}}^d)$
• Global well-posedness and equicontinuity for mKdV in modulation spaces
• On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces