Abstract
We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost automorphic solutions. Lastly, our abstract results are applied to the Navier-Stokes equations (NSE) on some different circumstances such as the NSE on exterior domains, around rotating obstacles, and in Besov spaces.
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The work of T. N. H. Vu was partly supported by the Project of the Vietnam Ministry of Education and Training under Project B2022-BKA-06. This work was financially supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2021.04.
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Nguyen, T.H., Vu, T.N.H., Le, T.S. et al. Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics. Czech Math J 72, 935–955 (2022). https://doi.org/10.21136/CMJ.2022.0002-21
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DOI: https://doi.org/10.21136/CMJ.2022.0002-21
Keywords
- linear evolution equation
- semilinear evolution equation
- almost automorphic function
- weighted pseudo almost automorphic function and solution
- interpolation space