On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation

van Duong Dinh (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove the local well-posedness for the nonlinear fourth-order Schrödinger equation (NL4S) in Sobolev spaces. We also study the regularity of solutions in the sub-critical case. A direct consequence of this regularity is the global well-posedness above mass and energy spaces under some assumptions. Finally, we show the ill-posedness for (NL4S) in some cases of the super-critical range.

Mots clés: fourth-order schrodinger; well-posedness; regularity; ill-posedness

Domaines: Equations aux dérivées partielles [math.AP]

van Duong Dinh. On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation. Bulletin of the Belgian Mathematical Society - Simon Stevin, 2018, 25 (3), pp.415-437. ⟨hal-01484204⟩