Existence and Smoothing Effect of Solutions for the Zakharov Equations | Zendy

Tohru Ozawa | Zendy; Yoshio Tsutsumi | Zendy

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Existence and Smoothing Effect of Solutions for the Zakharov Equations

Author(s) -

Tohru Ozawa,

Yoshio Tsutsumi

Publication year - 1992

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195168430

Subject(s) - smoothing , mathematics , envelope (radar) , function (biology) , electric field , turbulence , ion , mathematical physics , mathematical analysis , plasma , physics , thermodynamics , statistics , quantum mechanics , biology , telecommunications , radar , evolutionary biology , computer science

where E is a function from R* xR% to C9 n is a function from R^ xR% to R and 1<^JV<^3. (1. !)-(!. 3) describe the long wave Langmuir turbulence in a plasma (see [20]). E(t, x) denotes the slowly varying envelope of the highly oscillatory electric field and n(t, x) denotes the deviation of the ion density from its equilibrium. When (1.2) depends on the ion sound speed c, that is, (1.2) is replaced by

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