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arXiv · 2010.04309

Lifespan of solutions to the Strauss type wave system on asymptotically flat space-times

Wei Dai·Daoyuan Fang·Chengbo Wang
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Abstract

By assuming certain local energy estimates on $(1+3)$-dimensional asymptotically flat space-time, we study the existence portion of the \emph{Strauss} type wave system. Firstly we give a kind of space-time estimates which are related to the local energy norm that appeared in \cite{MR2944027}. These estimates can be used to prove a series of weighted \emph{Strichartz} and \emph{KSS} type estimates, for wave equations on asymptotically flat space-time. Then we apply the space-time estimates to obtain the lower bound of the lifespan when the nonlinear exponents $p$ and $q\ge 2$. In particular, our bound for the subcritical case is sharp in general and we extend the known region of $(p,q)$ to admit global solutions. In addition, the initial data are not required to be compactly supported, when $p, q>2$.

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Wei Dai, Daoyuan Fang, Chengbo Wang. 2020-10-09. Lifespan of solutions to the Strauss type wave system on asymptotically flat space-times. https://doi.org/10.3934/dcds.2020208

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