The Glassey conjecture with radially symmetric data

Abstract

In this paper, we verify the Glassey conjecture in the radial case for all spatial dimensions, which states that, for the nonlinear wave equations of the form $\square u=|\nabla u{|}^p$, the critical exponent to admit global small solutions is given by $p_c=1+\frac{2}{n-1}$. Moreover, we are able to prove the existence results with low regularity assumption on the initial data and extend the solutions to the sharp lifespan. The main idea is to exploit the trace estimates and KSS type estimates.

28 pages

References in corpus (2)

• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation
• Strichartz estimates for Dirichlet-wave equations in two dimensions with applications

Cited by in corpus (17)

• Test function method for blow-up phenomena of semilinear wave equations and their weakly coupled systems
• Combined effects of two nonlinearities in lifespan of small solutions to semi-linear wave equations
• A blow-up result for the semilinear Moore-Gibson-Thompson equation with nonlinearity of derivative type in the conservative case
• Blow-up and lifespan estimate for generalized Tricomi equations related to Glassey conjecture
• Global existence of null-form wave equations on small asymptotically Euclidean manifolds
• A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type
• Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case
• Global existence and lifespan for semilinear wave equations with mixed nonlinear terms
• The Glassey conjecture on asymptotically flat manifolds
• Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms
• A blow-up result for a generalized Tricomi equation with nonlinearity of derivative type
• A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime
• Blow-up for wave equation with the scale-invariant damping and combined nonlinearities
• Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type
• The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative
• On Glassey's conjecture for semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime
• Blow-up and lifespan estimates for Nakao's type problem with nonlinearities of derivative type