ON THE CAUCHY PROBLEM OF THE MODIFIED HUNTER-SAXTON EQUATION.

This paper is concerned with the Cauchy problem of the modified Hunter-Saxton equation, which was proposed by by J. Hunter and R. Saxton [SIAM J. Appl. Math. 51(1991) 1498-1521]. Using the approximate solution method, the local well-posedness of the model equation is obtained in Sobolev spaces H^s with s > 3=2, in the sense of Hadamard, and its data-to-solution map is continuous but not uniformly continuous. However, if a weaker H^r-topology is used then it is shown that the solution map becomes Hölder continuous in H^s. [ABSTRACT FROM AUTHOR]