Unconditional local well-posedness for periodic NLS

Abstract

The nonlinear Schrödinger equations with nonlinearities $|u{|}^{2k}u$ on the $d$-dimensional torus are considered for arbitrary positive integers $k$ and $d$. The solution of the Cauchy problem is shown to be unique in the class $C_t{H}_x^s$ for a certain range of scale-subcritical regularities $s$, which is almost optimal in the case $d\ge 4$ or $k\ge 2$. The proof is based on various multilinear estimates and the infinite normal form reduction argument.

arXiv comment18 pages. Version 2: Resubmitted after a failure in producing PDF

References in corpus (5)

• Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
• Instability of the periodic nonlinear Schrodinger equation
• Strichartz estimates for Schrödinger equations on irrational tori in two and three dimensions
• Unconditional uniqueness of solutions for nonlinear dispersive equations
• Incidence theory and restriction estimates

Cited by in corpus (1)

• The Unconditional Uniqueness for the Energy-critical Nonlinear Schrödinger Equation on ${\mathbb{T}}^4$