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Recent progress in attractors for quintic wave equations

Anton SavostianovSergey Zelik — 2014

Mathematica Bohemica

We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of 3 with damping terms of the form ( - Δ x ) θ t u , 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...

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