Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices

Author： Wang Hua  

Publisher： Springer Publishing Company

ISSN： 1439-8516

Source： Acta Mathematica Sinica, Vol.23, Iss.8, 2007-08, pp. : 1435-1446

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Abstract

We first prove that the Cauchy problem of the Kawahara equation, , is locally solvable if the initial data belong to H r (R) and , thus improving the known local well-posedness result of this equation. Next we use this local result and the method of "almost conservation law" to prove that global solutions exist if the initial data belong to H r (R) and - frac{1} {2}. $$]]>

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