# Inertial manifolds for 3D complex Ginzburg-Landau equations with periodic boundary conditions

@inproceedings{Kostianko2021InertialMF, title={Inertial manifolds for 3D complex Ginzburg-Landau equations with periodic boundary conditions}, author={Anna Kostianko and Chunyou Sun and Sergey Zelik}, year={2021} }

We prove the existence of an Inertial Manifold for 3D complex Ginzburg-Landau equation with periodic boundary conditions as well as for more general cross-diffusion system assuming that the dispersive exponent is not vanishing. The result is obtained under the assumption that the parameters of the equation is chosen in such a way that the finite-time blow up of smooth solutions does not take place. For the proof of this result we utilize the method of spatio-temporal averaging recently…

## One Citation

Inertial manifolds and foliations for asymptotically compact cocycles in Banach spaces

- Mathematics
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We study asymptotically compact nonautonomous dynamical systems given by abstract cocycles in Banach spaces. Our main assumptions are given by a squeezing property in a quadratic cone ﬁeld (given by…

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