Prefer a chat interface with context about you and your work?
On the critical exponent and sharp lifespan estimates for semilinear damped wave equations with data from Sobolev spaces of negative order
We study semilinear damped wave equations with power nonlinearity $|u|^p$ and initial data belonging to Sobolev spaces of negative order $\dot{H}^{-\gamma}$. In the present paper, we obtain a new critical exponent $p=p_{\mathrm{crit}}(n,\gamma):=1+\frac{4}{n+2\gamma}$ for some $\gamma\in(0,\frac{n}{2})$ and low dimensions in the framework of Soblev spaces of negative order. Precisely, global (in …