| Existence for Semilinear Wave Equations with Low Regularity |
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| 作者姓名： | YANG Ning YANG Han |
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| 作者单位： | Department of Mathematics，Southwest Jiaotong University，Chengdu 610031，China |
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| 基金项目： | Supported by the NSF of China(10225102, 10301026)，Supported by the South-west Jiaotong University Foundation(20005B05) |
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| 摘 要： | In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-Δu=F(u, Du), u(0, x)=f(x)∈HS,(?)tu(0, x)=g(x)∈HS-1, where F is quadratic in Du with D = ((?)t,(?)x1,…,(?)xn). We proved that the range of s is s≥n 1/2 δ, respectively, withδ>1/4 if n = 2, andδ>0 if n = 3, andδ≥0 if n≥4. Which is consistent with Lindblad's counterexamples 3] for n = 3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.
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| 关 键 词： | 准线性波方程 局部存在性 低规律性 初始数据 |
Existence for Semilinear Wave Equations with Low Regularity |
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| YANG Ning,YANG Han.Existence for Semilinear Wave Equations with Low Regularity[J].Chinese Quarterly Journal of Mathematics,2006,21(1):49-56. |
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| Authors: | YANG Ning YANG Han |
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| Institution: | Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, China |
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| Abstract: | |
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| Keywords: | semilinear wave equations local existence low regularity |
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