2017年9月
SCATTERING AND WELL-POSEDNESS FOR THE ZAKHAROV SYSTEM AT A CRITICAL SPACE IN FOUR AND MORE SPATIAL DIMENSIONS
DIFFERENTIAL AND INTEGRAL EQUATIONS
- ,
- 巻
- 30
- 号
- 9-10
- 開始ページ
- 763
- 終了ページ
- 794
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- 出版者・発行元
- KHAYYAM PUBL CO INC
We study the Cauchy problem for the Zakharov system in spatial dimension d >= 4 with initial datum (u(0), n(0), partial derivative(t)n(0)) is an element of H-k(R-d) x (H) over dot(l) (R-d) x (H) over dot(l-1)(R-d). According to Ginibre, Tsutsumi and Velo ([9]), the critical exponent of (k, l) is ((d - 3)/2, (d - 4)/2). We prove the small data global well-posedness and the scattering at the critical space. It seems difficult to get the crucial bilinear estimate only by applying the U-2, V-2 type spaces introduced by Koch and Tataru ([23], [24]). To avoid the difficulty, we use an intersection space of V-2 type space and the space-time Lebesgue space E := (LtLx2d/(d-2))-L-2, which is related to the endpoint Strichartz estimate.
- リンク情報
- ID情報
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- ISSN : 0893-4983
- Web of Science ID : WOS:000406354100005