Well-posedness and attractors for the sub-quintic weakly damped wave equation with low-regularity forcing on $\mathbb{R}^3$
Year: 2026
Type: preprint
Abstract: We study the weakly damped semilinear wave equation on $\mathbb{R}^3$ with a sub-quintic nonlinearity $f(u)$ and a forcing term of low regularity, $g\in H^{-1}(\mathbb{R}^3)$. By absorbing the forcing term into a stationary solution $h$ and then expanding the solution around $h$, we reduce the problem to a wave equation with potentials. Relying on Strichartz estimates for this equation, obtained through the Besov spaces associated with the Schrödinger operator, we establish the global well-posedness of weak solutions by an iteration argument on the Besov scale. In particular, uniqueness holds unconditionally in the energy class for $3
Source: arXiv (Cornell University)
Authors: Meng, Fengjuan, Liu, Cuncai, Sun, Chunyou
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225755375