English

Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus

Analysis of PDEs 2012-02-16 v1

Abstract

We consider the time local and global well-posedness for the fourth order nonlinear Schrodinger type equation (4NLS) on the torus. The nonlinear term of (4NLS) contains the derivatives of unknown function and this prevents us to apply the classical energy method. To overcome this difficulty, we introduce the modified energy and derive an a priori estimate for the solution to (4NLS).

Keywords

Cite

@article{arxiv.1202.3211,
  title  = {Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus},
  author = {Jun-ichi Segata},
  journal= {arXiv preprint arXiv:1202.3211},
  year   = {2012}
}