On Strichartz estimates from decoupling and applications

Abstract

Strichartz estimates are derived from ${\ell }^2$-decoupling for phase functions satisfying a curvature condition. Bilinear refinements without loss in the high frequency are discussed. Estimates are established from uniform curvature generalizing Galilean invariance or from transversality in one dimension. The bilinear refinements are utilized to prove local well-posedness for generalized cubic nonlinear Schrödinger equations.

7 pages, minor mathematical mistakes corrected

References in corpus (2)

• Strichartz estimates for the fractional Schrödinger and wave equations on compact manifolds without boundary
• On shorttime bilinear Strichartz estimates and applications to improve the energy method

Cited by in corpus (3)

• On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations
• Local and global well-posedness of dispersion generalized Benjamin-Ono equations on the circle
• Singular Levy processes and dispersive effects of generalized Schrödinger equations