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S 2 ( H ):= {$ : [O,T]x R -+ H , cadlag, adapted and such that IE [ SUP (eYCtI4(t)l&)]< > .. OltlT MfO,T](H) := { N E MfO,T](H)? IE [JTeYctd ( N ) , ]< O0}' B 2 ( H ) := Lg(O,T;H ) x A 2 ( H ;P , M ) . Then B 2 ( H )is a separable Hilbert space with the norm A solution of (3) is a triple (Y,2,N ) E B 2 ( H )x hfO,T1(H) such that for all t E [O,T],we have a s . O. The main result is the following theorem. 1. Suppose that (Hl)-(H5) hold with a parameter y being large enough. Then there exists a unique solution (Y,2,N ) E B 2 ( H )xMf0,,,(H) of (3).

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A blow-up result for the periodic Camassa-Holm equation by Wahlen E.

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