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Scattering for defocusing energy subcritical nonlinear wave equations

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arxiv 1810.03182 v3 pith:XKBBRWL4 submitted 2018-10-07 math.AP

Benjamin Dodson , Andrew Lawrie , Dana Mendelson , Jason Murphy This is my paper · ORCID
classification math.AP
keywords defocusingenergynonlinearsubcriticalwaveboundedcauchyconsider
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abstract

We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1+3)$-dimensions for energy subcritical powers $p$ in the range $3 < p< 5$. We prove that any solution is global-in-time and scatters to free waves in both time directions as long as its critical Sobolev norm stays bounded on the maximal interval of existence.

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  1. Global behaviors of defocusing semilinear wave equations

    math.AP 2019-08 conditional novelty 7.0 of 10

    Defocusing semilinear wave equations in dimension d at least 3 satisfy integrated local energy decay for all energy-subcritical and critical powers, and scatter for powers above 1 + sqrt(d^2 + 4d - 4) / (d - 1) withou...

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