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arXiv · 1703.00891

Well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schr\"odinger equation

Van Duong Dinh
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Abstract

We prove the local well-posedness for the nonlinear fourth-order Schr\"odinger equation (NL4S) in Sobolev spaces. We also studied 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.

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Van Duong Dinh. 2017-03-02. Well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schr\"odinger equation. https://arxiv.org/abs/1703.00891

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