An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation

  • Tohru Ozawa

    Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan
  • Nicola Visciglia

    Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy

Abstract

We revise the classical approach by Brézis–Gallouët to prove global well-posedness for nonlinear evolution equations. In particular we prove global well-posedness for the quartic NLS on general domains Ω in with initial data in , and for the quartic nonlinear half-wave equation on with initial data in .

Cite this article

Tohru Ozawa, Nicola Visciglia, An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 4, pp. 1069–1079

DOI 10.1016/J.ANIHPC.2015.03.004