Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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REMARKS ON THE EXISTENCE OF AN INERTIAL MANIFOLD

  • Kwak, Minkyu (Department of Mathematics Chonnam National University) ;
  • Sun, Xiuxiu (Department of Mathematics Chonnam National University)
  • Received : 2020.10.12
  • Accepted : 2020.11.05
  • Published : 2021.09.01
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Abstract

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

Keywords

Acknowledgement

This work was supported by Basic Science Research Program through NRF, 2017R1E1A1A03070061.

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