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ファイル | 記述 | サイズ | フォーマット | |
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B65-03.pdf | 9.85 MB | Adobe PDF | 見る/開く |
タイトル: | Regularity and lifespan of small solutions to systems of quasi-linear wave equations with multiple speeds, I: almost global existence (Harmonic Analysis and Nonlinear Partial Differential Equations) |
著者: | Hidano, Kunio |
著者名の別形: | ヒダノ, クニオ |
キーワード: | 35L72 almost global existence system of nonlinear wave equations multiple propagation speeds |
発行日: | May-2017 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B65 |
開始ページ: | 37 |
終了ページ: | 61 |
抄録: | In this paper, we show almost global existence of small solutions to the Cauchy problem for symmetric system of wave equations with quadratic (in 3D) or cubic (in 2D) nonlinear terms and multiple propagation speeds. To measure the size of initial data, we employ a weighted Sobolev norm whose regularity index is the smallest among all the admissible Sobolev norms of integer order. We must overcome the difficulty caused by the absence of the H1-Lp Klainerman-Sobolev type inequality, in order to obtain a required a priori bound in the low-order Sobolev norm. The introduction of good substitutes for this inequality is therefore at the core of this paper. Using the idea of showing the well-known Lady zenskaja inequality, we prove some weighted inequalities, which, together with the generalized Strauss inequality, play a role as the good substitute. |
記述: | "Harmonic Analysis and Nonlinear Partial Differential Equations". July 4~6, 2016. edited by Hideo Kubo and Hideo Takaoka. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2017 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/243680 |
出現コレクション: | B65 Harmonic Analysis and Nonlinear Partial Differential Equations |
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