Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

AN INERTIAL MANIFOLD FOR A NON-SELF ADJOINT SYSTEM

  • Sun, Xiuxiu (Department of Mathematics & Statistics, Chonnam National University)
  • Received : 2020.10.08
  • Accepted : 2020.11.20
  • Published : 2020.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this work, we prove an existence of an inertial manifold for a system of differential equations with a non-self adjoint leading part. The result follows from the existence and uniqueness of negatively bounded solutions. In fact, we show that a sharp spectral condition is sufficient for the proof.

Keywords

References

  1. Z. Fang and M. Kwak, A finite dimensional property of a parabolic partial differential equation, J. Dynam. Diff. Eqns 17 (2005), 845-855. https://doi.org/10.1007/s10884-005-8272-y
  2. Z. Fang and M. Kwak, Negatively bounded solutions for a parabolic partial differential equation, Bull. Korean Math. Soc. 42 (2005), 829-836. https://doi.org/10.4134/BKMS.2005.42.4.829
  3. C. Foias, G. Sell and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Diff. Eqns 73 (1988), 309-353. https://doi.org/10.1016/0022-0396(88)90110-6
  4. A. Kostianko and S. Zelik, Kwak transform and inertial manifolds revisited, arXiv preprint arXiv:1911.00698 (2019).
  5. M. Kwak, Finite dimensional inertial forms for 2D Navier-Stokes equations, Indiana Univ. Math. J. 41 (1992), 927-982. https://doi.org/10.1512/iumj.1992.41.41051
  6. M. Kwak and X. Sun, Remarks on the existence of an inertial manifold, (2020), accepted.
  7. R. Temam, Infinite-dimensional dynamical systems in mechnics and physics, Applied Math. Science 68 (1997), Springer.
  8. S. Zelik, Inertial manifolds and finite-dimensional reduction for dissipative PDEs, Proc R Soc Lond Ser A 144A (2014), 1245-1327.