Global Well-posedness and Scattering of Defocusing Energy subcritical Nonlinear Wave Equation in dimension 3 with radial data

Abstract

The paper deals with the defocusing case of the energy subcritical non-linear wave equation in $R^3$. We assume the initial data is in the space ${\dot{H}}^s\times {\dot{H}}^{s-1}$ and radial. If $s=1$, this is the energy space and the scattering results are known. In this paper we choose $15/16<s<1$ and assume that the nonlinearity equals $-|u{|}^{p}u$ with $p=2/3/2-s$, so that this problem is ${\dot{H}}^s\times {\dot{H}}^{s-1}$ critical. We will prove the global well-posedness and scattering of the solution under the additional assumption that the ${\dot{H}}^s\times {\dot{H}}^{s-1}$ norm of the solution is uniformly bounded for all time $t$ in the maximal lifespan of the solution.

References in corpus (1)

• Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications

Cited by in corpus (2)

• The defocusing energy-supercritical NLS in four space dimensions
• Inter-critical NLS: critical ${\dot{H}}^s$-bounds imply scattering