Smooth attractors for the quintic wave equations with fractional damping
Analysis of PDEs
2013-06-11 v1
Abstract
Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.
Keywords
Cite
@article{arxiv.1306.2294,
title = {Smooth attractors for the quintic wave equations with fractional damping},
author = {Anton Savostianov and Sergey Zelik},
journal= {arXiv preprint arXiv:1306.2294},
year = {2013}
}