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报告题目：Cauchyproblem for a generalized cross-coupled Camassa-Holm system withwaltzing peakons and higher-order nonlinearities
报告人：穆春来教授（重庆大学）
报告时间：2016年6月17日（星期五）下午2:30-3:30
报告地点：4号楼4318室

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                                                                     数学学院
                                                                  2016年06月16日
报告摘要：
  In this talk, we study the Cauchy problem for a generalizedcross-coupled Camassa-Holm system with peakons and higher-ordernonlinearities. By the transport equation theory and the classicalFriedrichs regularization method, we obtain the local well-posednessof solutions for the system in nonhomogeneous Besov spaces B^s_{p,r}× B^s_{p,r} with 1 ≤ p, r ≤ +∞ and s > max{2 + 1/p , 5/2}.Moreover, we construct the local well-posedness in the critical Besovspace B^{5/2}_{2,1} × B^{5/2}_{2,1} and the blow-up criteria. Wealso consider the well-posedness problem in the sense of Hadamard,non-uniform dependence, and H¨older continuity of thedata-to-solution map for the system on both the periodic and thenon-periodic case. In light of a Galerkin-type approximation scheme,the system is shown well-posed in the Sobolev spaces H^s×H^s, s >5/2 in the sense of Hadamard, that is, the data-to-solution map iscontinuous. However, the solution map is not uniformly continuous.Furthermore, we prove the H¨older continuity in the H^r×H^rtopology when 0 ≤ r < s with H¨older exponent α depending onboth s and r.