Concerning the Strauss conjecture on asymptotically Euclidean manifolds

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 $0<μ<1/2$ and weighted Strichartz estimates of order two.

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