Recent progress in attractors for quintic wave equations

Title:

Recent progress in attractors for quintic wave equations

Creator:

Savostianov, Anton and Zelik, Sergey

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:82c45474-078f-4c89-8c34-329545f7a163
uuid:82c45474-078f-4c89-8c34-329545f7a163
doi:10.21136/MB.2014.144142

Subject:

damped wave equation, fractional damping, critical nonlinearity, global attractor, and smoothness

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

657-665

Source:

Mathematica bohemica | 2014 Volume:139 | Number:4

Harvested from:

CDK

Metadata only:

false