1. Recent progress in attractors for quintic wave equations
- Creator:
- Savostianov, Anton and Zelik, Sergey
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- damped wave equation, fractional damping, critical nonlinearity, global attractor, and smoothness
- Language:
- English
- Description:
- We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of R 3 with damping terms of the form (−∆x) θ ∂tu, where θ = 0 or θ = 1/2. The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when θ = 1/2. For θ = 0 existence of smooth attractors is more complicated and follows from Strichartz type estimates.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public