ON THE INITIAL VALUE PROBLEM FOR HIGHER DIMENSIONAL CAMASSA-HOLM EQUATIONS

摘要

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.