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) without spherical symmetry.
Scattering for defocusing energy subcritical nonlinear wave equations
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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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Global behaviors of defocusing semilinear wave equations
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) without spherical symmetry.