Sharp Global Existence for Semilinear Wave Equation with Small Data

2006/12/10 by Daoyuan Fang, Chengbo Wang, Fang, Daoyuan +1
Mathematics · Physics and Astronomy · #35A05 #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #math.AP #msc:35A05 #msc:35L70

paper · pdf · doi:10.48550/arxiv.math/0612249

4 pages, version 3, the sharpness for the result is explained

openalex publication_date 2006/12/10 · arxiv created 2007/03/12 · arxiv updated 2010/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using the Strichartz esitmate and Picard iteration, we prove the subcritical(critical in some cases) global solution in C_t H_x^s∩ C_t¹ H^s-1_x with small data for semilinear wave equation with nonlinearity of type (∂ u)^k(k≥ 1+(4)/(n-1)\vee 2 and (n,k)≠ (3,3)). For (n,k)=(3,3), we get the almost global existence. In addition, we give the global existence with radial data when k> 1+(2)/(n-1)\vee 2.

Citations

• Uniform decay estimates and the lorentz invariance of the classical wave equation

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