Title: On a dissipative form of Camassa–Holm equation
Abstract:In this paper, we consider several problems on the Camassa–Holm equation with a weak dissipation term. First, we establish the local well-posedness result and then we present several new blow-up resul...In this paper, we consider several problems on the Camassa–Holm equation with a weak dissipation term. First, we establish the local well-posedness result and then we present several new blow-up results and discuss the global existence of the solution for the periodic case. Finally, we examine the persistence of decay properties for the weakly dissipative Camassa–Holm equation, and we prove that any nontrivial classical solution of the equation will not have compact support if its initial data have this property.Read More