The Local Strong and Weak Solutions for a Nonlinear Dissipative Camassa-Holm Equation

الملخص EN

Using the Kato theorem for abstract differential equations, the local well-posedness of the solution for a nonlinear dissipative Camassa-Holm equation is established in space C([0,T),Hs(R))∩C1([0,T),Hs-1(R)) with s>3/2.

In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space Hs(R) with 1≤s≤3/2 is developed.