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首页> 外文期刊>Annali Dell Universita di Ferrara, Sezione VII. Scienze Matematiche >Attractors for Navier–Stokes equation with fractional operator in the memory term
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Attractors for Navier–Stokes equation with fractional operator in the memory term

机译：Attractors for Navier–Stokes equation with fractional operator in the memory term

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Abstract In this paper, we study the long-time dynamics of Navier–Stokes equations with a fractional operator in the memory term and external forces ?tu-νΔu+∫0∞g(s)(-Δ)αu(t-s)ds+(u·?)u+?p=?f(x)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$begin{aligned} partial _tu-nu Delta u +displaystyle int _{0}^{infty }g(s)(-Delta )^alpha u(t-s),mathrm{d}s +(ucdot nabla )u+nabla p=epsilon f(x) end{aligned}$$end{document}on a bounded domain Ωdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Omega $$end{document} in R2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {R}^2$$end{document} with smooth boundary. We establish the existence of global attractor for the associated dynamical system. We prove the continuity of global attractors with respect to forcing parameter ?documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$epsilon $$end{document} in a residual dense set. Moreover, the upper-semicontinuity with respect to parameter ?documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$epsilon $$end{document} of global attractors is shown.

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