Global Conservative Solutions of the Camassa–holm Equation — a Lagrangian Point of View
نویسنده
چکیده
Abstract. We show that the Camassa–Holm equation ut −uxxt +3uux −2uxuxx −uuxxx = 0 possesses a global continuous semigroup of weak conservative solutions for initial data u|t=0 in H. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure μ with μac = (u + u2x) dx.
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