Abstract
We prove the local well-posedness for the nonlinear fourth-order Schrödinger equation (NL4S) in Sobolev spaces. We also study the regularity of local 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.
Citation
Van Duong Dinh. "On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation." Bull. Belg. Math. Soc. Simon Stevin 25 (3) 415 - 437, september 2018. https://doi.org/10.36045/bbms/1536631236
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