ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO STOCHASTIC 3D GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS WITH UNBOUNDED DELAYS

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO STOCHASTIC 3D GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS WITH UNBOUNDED DELAYS

This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space BCL-∞(H). We first prove the existence and uniqueness of weak solutions by using the classical technique of...

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Veröffentlicht in:Journal of the Korean Mathematical Society 2024, Vol.61 (2), p.227-253
Hauptverfasser: Cung The Anh, Vu Manh Toi, Phan Thi Tuyet
Format: Artikel
Sprache:kor
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Zusammenfassung:This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space BCL-∞(H). We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.
ISSN:0304-9914