Inward/outward Energy Theory of Wave Equation in Higher Dimensions

Abstract

We consider the semi-linear, defocusing wave equation ${\partial }_t^{2}u-\Delta u=-|u{|}^{p-1}u$ in ${\mathbb{R}}^d$ with $1+4/(d-1)\le p<1+4/(d-2)$. We generalize the inward/outward energy theory and weighted Morawetz estimates in 3D to higher dimensions. As an application we show the scattering of solutions if the energy of initial data decays at a certain rate as $|x|\to \infty$.

arXiv comment24 pages, 2 figures

References in corpus (2)

• Scattering for the radial 3d cubic wave equation
• Scattering of solutions to NLW by Inward Energy Decay

Cited by in corpus (4)

• Scattering theory for subcritical wave equation with inverse square potential
• Exterior scattering of non-radial solutions to energy subcritical wave equations
• Asymptotic energy distribution of one-dimensional nonlinear wave equation
• Energy distribution of solutions to defocusing semi-linear wave equation in higher dimensional space