On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces

Van Duong Dinh

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arXiv · 1701.00852

On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces

Van Duong Dinh

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Abstract

We proved the local well-posedness for the power-type nonlinear semi-relativistic or half-wave equation (NLHW) in Sobolev spaces. Our proofs mainly bases on the contraction mapping argument using Strichartz estimate. We also apply the technique of Christ-Colliander- Tao in \cite{ChristCollianderTao} to prove the ill-posedness for (NLHW) in some cases of the super-critical range.

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Van Duong Dinh. 2017-01-03. On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces. https://arxiv.org/abs/1701.00852

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