Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics

Thieu Huy Nguyen; Thi Ngoc Ha Vu; The Sac Le; Truong Xuan Pham

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 4, page 935-955
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Nguyen, Thieu Huy, et al. "Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics." Czechoslovak Mathematical Journal 72.4 (2022): 935-955. <http://eudml.org/doc/298926>.

@article{Nguyen2022,
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.},
author = {Nguyen, Thieu Huy, Vu, Thi Ngoc Ha, Le, The Sac, Pham, Truong Xuan},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear evolution equation; semilinear evolution equation; almost automorphic function; weighted pseudo almost automorphic function and solution; interpolation space},
language = {eng},
number = {4},
pages = {935-955},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics},
url = {http://eudml.org/doc/298926},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Nguyen, Thieu Huy
AU - Vu, Thi Ngoc Ha
AU - Le, The Sac
AU - Pham, Truong Xuan
TI - Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 935
EP - 955
AB - 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.
LA - eng
KW - linear evolution equation; semilinear evolution equation; almost automorphic function; weighted pseudo almost automorphic function and solution; interpolation space
UR - http://eudml.org/doc/298926
ER -

References

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