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Global existence of weak solutions for a shallow water equation. (English) Zbl 1205.76049
Summary: A nonlinear shallow water equation, which includes the famous Camassa-Holm (CH) and Degasperis-Procesi (DP) equations as special cases, is investigated. Provided that initial value u 0 H s (1s3 2), u o L 1 (R) and (1-δ x 2 )u 0 does not change sign, it is shown that there exists a unique global weak solution to the equation.

MSC:
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
35Q35PDEs in connection with fluid mechanics
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