Geodesic
Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 935-955.

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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.
DOI : 10.21136/CMJ.2022.0002-21
Classification : 35B15, 35B35, 35Q30, 76D05
Keywords: linear evolution equation; semilinear evolution equation; almost automorphic function; weighted pseudo almost automorphic function and solution; interpolation space 
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Nguyen, Thieu Huy; Vu, Thi Ngoc Ha; Le, The Sac; Pham, Truong Xuan. Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 935-955. doi : 10.21136/CMJ.2022.0002-21. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0002-21/

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