Critical local well-posedness of the nonlinear Schrödinger equation on the torus

  • Beomjong Kwak

    Korea Advanced Institute of Science and Technology, Daejeon, South Korea
  • Soonsik Kwon

    Korea Advanced Institute of Science and Technology, Daejeon, South Korea
Critical local well-posedness of the nonlinear Schrödinger equation on the torus cover

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Abstract

In this paper, we study the local well-posedness of nonlinear Schrödinger equations on tori at the critical regularity. We focus on cases where the nonlinearity is nonalgebraic with small . We prove the local well-posedness for a wide range covering the mass-supercritical regime. Moreover, we supplementarily investigate the regularity of the solution map. In pursuit of lowering , we prove a bilinear estimate for the Schrödinger operator on tori , which enhances previously known multilinear estimates. We design a function space adapted to the new bilinear estimate and a package of Strichartz estimates, which is not based on conventional atomic spaces.

Cite this article

Beomjong Kwak, Soonsik Kwon, Critical local well-posedness of the nonlinear Schrödinger equation on the torus. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first

DOI 10.4171/AIHPC/137