Document Zbl 1328.35167

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Math. Fluid Mech.</a> <a href="/?q=in%3A344715" title="Articles in this Issue">17, No. 2, 233-259 (2015)</a>. </div> <div class="abstract">Summary: We investigate the long-term behavior, as a certain regularization parameter vanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelastic incompressible fluid. We prove the existence of global and exponential attractors of optimal regularity. We then derive explicit upper bounds for the dimension of these attractors in terms of the three-dimensional Grashof number and the regularization parameter. Finally, we also prove convergence of the (strong) global attractor of the 3D Navier-Stokes-Voigt model to the (weak) global attractor of the 3D Navier-Stokes equation. Our analysis improves and extends recent results obtained by <span class="zbmathjax-textit">V. K. Kalantarov</span> and <span class="zbmathjax-textit">E. S. Titi</span> [Chin. Ann. Math., Ser. B 30, No. 6, 697–714 (2009; <a href="/1178.37112">Zbl 1178.37112</a>)].</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6508164">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A6508164">Cited in <strong>31</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q35" title="MSC2020">35Q35</a> </td> <td class="space"> PDEs in connection with fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37L30" title="MSC2020">37L30</a> </td> <td class="space"> Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q30" title="MSC2020">35Q30</a> </td> <td class="space"> Navier-Stokes equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B40" title="MSC2020">35B40</a> </td> <td class="space"> Asymptotic behavior of solutions to PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B41" title="MSC2020">35B41</a> </td> <td class="space"> Attractors </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B65" title="MSC2020">35B65</a> </td> <td class="space"> Smoothness and regularity of solutions to PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76A10" title="MSC2020">76A10</a> </td> <td class="space"> Viscoelastic fluids </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ANavier-Stokes-Voigt+equations">Navier-Stokes-Voigt equations</a>; <a href="/?q=ut%3Aglobal+attractor">global attractor</a>; <a href="/?q=ut%3Aexponential+attractor">exponential attractor</a>; <a href="/?q=ut%3Aregularization+of+Navier-Stokes+equations">regularization of Navier-Stokes equations</a>; <a href="/?q=ut%3Aturbulence+models">turbulence models</a>; <a href="/?q=ut%3Aviscoelastic+models">viscoelastic models</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1178.37112">Zbl 1178.37112</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1328.35167" data-ciurl="/ci/06508164" data-biburl="/bibtex/06508164.bib" data-amsurl="/amsrefs/06508164.bib" data-xmlurl="/xml/06508164.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06508164.pdf" title="Zbl 1328.35167 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s00021-015-0201-1" aria-label="DOI for “Singular limits of Voigt models in fluid dynamics”" title="10.1007/s00021-015-0201-1">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1408.3497"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ball J.M.: Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations. 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