Funkcialaj Ekvacioj
Print ISSN : 0532-8721
Uniqueness of Solutions for Zakharov Systems
Nader MasmoudiKenji Nakanishi
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2009 Volume 52 Issue 2 Pages 233-253

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Abstract

We prove that the weak solution of the Cauchy problem for the Klein-Gordon-Zakharov system and for the Zakharov system is unique in the energy space for the former system, and in some larger space for the latter system, in dimensions three or lower. In the three dimensional case, these are the largest Sobolev spaces where the local wellposedness has been proven so far. Our proof uses infinite iteration, where the solution is fixed but the function spaces are converging to the desired ones in the limit.

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© 2009 by the Division of Functional Equations, The Mathematical Society of Japan
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