Abstract
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.
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