Regularity Structure of Conservative Solutions to the Hunter--Saxton Equation

In this paper we characterize the regularity structure, as well show global-in-time existence and uniqueness, of (energy) conservative solutions to Hunter-Saxton equation by using method characteristics. The major difference between current work previous results is that are able singularities energy measure their nature in a very precise manner. particular, singularities, whose temporal spatial locations also explicitly given work, may only appear at most countably many times, completely determined absolutely continuous part initial measure. Our mathematical analysis based on characteristics generalized framework consists evolutions solution This provides clear description semi-group property for all times.