MR2547104 Nader MASMOUDI and Kenji NAKANISHI Nader MASMOUDI and Kenji NAKANISHI Uniqueness of Solutions for Zakharov Systems Funkcialaj Ekvacioj. Serio Internacia 52 2009 233--253 http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-2/52_233.pdf http://www.ams.org/mathscinet-getitem?mr=MR2547104 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. Zakharov system, Unconditional uniqueness. 35Q60, 76X05, 82D10, 35B30. 52-233 2009 Uniqueness of Solutions for Zakharov Systems Nader MASMOUDI and Kenji NAKANISHI Nader MASMOUDI and Kenji NAKANISHI
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