| ON THE EQUATION □φ = |vφ|2 IN FOUR SPACE DIMENSIONS |
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| 引用本文： | 周忆. ON THE EQUATION □φ = |vφ|2 IN FOUR SPACE DIMENSIONS[J]. 数学年刊B辑(英文版), 2003, 24(3) |
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| 作者姓名： | 周忆 |
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| 作者单位： | Institute of Mathematics, Fudan University, Shanghai 200433, China |
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| 基金项目： | 国家重点基础研究发展计划(973计划) |
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| 摘 要： | This paper considers the following Cauchy problem for semilinear wave equations in n spacedimensions□φ = F( φ),φ(0, x) = f(x), tφ(0, x) = g(x),The minimal value of s is determined such that the above Cauchy problem is locally well-posed in Hs. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n ≥ 5). The purpose of thispaper is to supplement with a proof in the case n = 2, 4.
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ON THE EQUATION □φ = |vφ|2 IN FOUR SPACE DIMENSIONS |
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| Abstract: | This paper considers the following Cauchy problem for semilinear wave equations in n spacedimensions□φ = F( φ),φ(0, x) = f(x), tφ(0, x) = g(x),The minimal value of s is determined such that the above Cauchy problem is locally well-posed in Hs. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n ≥ 5). The purpose of thispaper is to supplement with a proof in the case n = 2, 4. |
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| Keywords: | Semilinear wave equation Cauchy problem Low regularity solution |
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