Concerning the Strauss conjecture on asymptotically Euclidean manifolds

TL;DR

This paper proves the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds in dimensions 3 and 4, providing lifespan estimates in the subcritical case using advanced analytical techniques.

Contribution

It verifies the Strauss conjecture in new geometric settings and offers near-optimal lifespan estimates for subcritical cases, employing novel weighted Strichartz and KSS estimates.

Findings

Strauss conjecture verified for n=3,4

Provides lifespan estimates for subcritical p

Utilizes weighted Strichartz and KSS estimates

Abstract

In this paper we verify the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds when n=3,4, we also give an almost sharp life span for the subcritical case $2\le p<p_c$ when n=3. The main ingredients include a KSS type estimate with $0<\mu<1/2$ and weighted Strichartz estimates of order two.