Generalized Strichartz Estimates on Perturbed Wave Equation and Applications on Strauss Conjecture

Abstract

In this paper we show a general Strichartz estimate for certain perturbed wave equation, and here we can drop the nontrapping hypothesis and handle trapping obstacles with some loss of derivatives for data in the local energy decay estimates. Then we give the obstacle version of sharp life span for semilinear wave equations when $n=3,p<p_c$, by using a real interpolation method, and by getting a corresponding finite time Strichartz estimates(see section 3). Finally, as an application of the general Strichartz estimates we have gained, we get the Strauss conjecture for semilinear wave equations with several convex obstacles when $n=3,4$(see Section 4).

To appear in Differential and Integral Equations

References in corpus (2)

• Global Strichartz estimates for nontrapping perturbations of the Laplacian
• Applications of Cutoff Resolvent Estimates to the Wave Equation

Cited by in corpus (8)

• The Strauss conjecture on Kerr black hole backgrounds
• Generalized and weighted Strichartz estimates
• Long time existence for semilinear wave equations on asymptotically flat space-times
• Recent works on the Strauss conjecture
• Concerning the Strauss conjecture on asymptotically Euclidean manifolds
• Lifespan estimates for $2$-dimensional semilinear wave equations in asymptotically Euclidean exterior domains
• Finite time blowup of solutions to semilinear wave equation in an exterior domain
• Global existence for a coupled wave system related to the Strauss conjecture