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On the initial value problem for higher dimensional Camassa-Holm equations

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  • This paper is concerned with the the initial value problem for higher dimensional Camassa-Holm equations. Firstly, the local well-posedness for this equations in both supercritical and critical Besov spaces are established. Then two blow-up criterions of strong solutions to the equations are derived. Finally, the analyticity of its solutions is proved in both variables, globally in space and locally in time.
    Mathematics Subject Classification: Primary: 35Q35, 35Q51; Secondary: 35L30.

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