Infinite energy solutions for weakly damped quintic wave equations in \(\mathbb{R}^3\). (English) Zbl 1460.35040
Summary: The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in \(\mathbb{R}^3\) with quintic nonlinearities. This study includes global well-posedness of the so-called Shatah-Struwe solutions, their dissipativity, the existence of a locally compact global attractors (in the uniformly local phase spaces) and their extra regularity.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B41 | Attractors |
| 35B45 | A priori estimates in context of PDEs |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35L15 | Initial value problems for second-order hyperbolic equations |
Keywords:
fractional damping; global attractor; unbounded domain; Strichartz estimates; Shatah-Struwe solutionsReferences:
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