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

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  • We proved the local well-posedness for the power-type nonlinear semi-relativistic or half-wave equation (NLHW) in Sobolev spaces. Our proofs are mainly based on the contraction mapping argument using Strichartz estimates. We also apply the technique of Christ-Colliander-Tao in [6] to prove the ill-posedness for the (NLHW) in a certain range of the super-critical case.

    Mathematics Subject Classification: Primary: 35A01, 35E15; Secondary: 35Q55.

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