Smooth attractors for the quintic wave equations with fractional damping

TL;DR

This paper proves the existence of smooth global and exponential attractors for dissipative wave equations with critical quintic nonlinearity and fractional damping, establishing regularity, well-posedness, and dissipativity.

Contribution

It introduces a new Lyapunov-type functional to demonstrate regularity and attractors for fractional damping wave equations with critical nonlinearity.

Findings

Existence of smooth global attractors

Finite Hausdorff and fractal dimension of attractors

Global well-posedness and dissipativity

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.