Uniform bound for solutions of semilinear wave equations in $\mathbb{R}^{1+3}$

Shiwu Yang

Uniform bound for solutions of semilinear wave equations in $\mathbb{R}^{1+3}$

Analysis of PDEs 2021-04-26 v3

Authors: Shiwu Yang

Abstract

We prove that solution of defocusing semilinear wave equation in $\mathbb{R}^{1+3}$ with pure power nonlinearity is uniformly bounded for all $\frac{3}{2}<p\leq 2$ with sufficiently smooth and localized data. The result relies on the $r$ -weighted energy estimate originally introduced by Dafermos and Rodnianski. This appears to be the first result regarding the global asymptotic property for the solution with small power $p$ under 2.

Keywords

semilinear wave equation uniform bound pure power nonlinearity r-weighted energy estimate global asymptotics

Cite

@article{arxiv.1910.02230,
  title  = {Uniform bound for solutions of semilinear wave equations in $\mathbb{R}^{1+3}$},
  author = {Shiwu Yang},
  journal= {arXiv preprint arXiv:1910.02230},
  year   = {2021}
}

Comments

Not for publication, the result has been combined in arXiv:1908.00607

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