Document Zbl 1507.35187

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(2020)</a>. </div> <div class="abstract">Summary: For $\nu \in (0, 1)$, we analyze the system of equations on the two dimensional domain $\Omega$ in the unknown function $u = (u_1(x, t), u_2(x, t))$ \[ \begin{cases} u_t - \mu\varDelta u - \gamma\varDelta\partial_t^\nu u + u\cdot\nabla u \\ = -\nabla p + f, \operatorname{div}u = 0, \end{cases} \] where $\partial_t^\nu$ denotes the Riemann-Liouville fractional derivative of order $\nu$. Under suitable conditions on the given data, the global existence and uniqueness of strong solutions to the related initial-boundary value problems are established for $\nu\in(0, 1/2)$. The convergence of the strong solution to the one of the corresponding initial-boundary value problem to the Navier-Stokes equations is discussed, in the limit $\nu \to 0$. We also present several numerical tests illustrating this convergence.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7507342">Cited in <strong>8</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%3A76A05" title="MSC2020">76A05</a> </td> <td class="space"> Non-Newtonian fluids </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76D05" title="MSC2020">76D05</a> </td> <td class="space"> Navier-Stokes equations for incompressible viscous fluids </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35D35" title="MSC2020">35D35</a> </td> <td class="space"> Strong solutions to PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A01" title="MSC2020">35A01</a> </td> <td class="space"> Existence problems for PDEs: global existence, local existence, non-existence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A02" title="MSC2020">35A02</a> </td> <td class="space"> Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M99" title="MSC2020">65M99</a> </td> <td class="space"> Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R11" title="MSC2020">35R11</a> </td> <td class="space"> Fractional partial differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ARiemann-Liouville+derivative">Riemann-Liouville derivative</a>; <a href="/?q=ut%3Afractional+generalized+second+grade+fluid">fractional generalized second grade fluid</a>; <a href="/?q=ut%3Asubdiffusive+Navier-Stokes-Voigt+equations">subdiffusive Navier-Stokes-Voigt equations</a>; <a href="/?q=ut%3Astrong+solutions">strong solutions</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 1507.35187" data-ciurl="/ci/07507342" data-biburl="/bibtex/07507342.bib" data-amsurl="/amsrefs/07507342.bib" data-xmlurl="/xml/07507342.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07507342.pdf" title="Zbl 1507.35187 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/10.1016/j.physd.2020.132503" aria-label="DOI for “A subdiffusive Navier-Stokes-Voigt system”" title="10.1016/j.physd.2020.132503">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Sloninsky, G., Laws of mechanical relaxation processes in polymer, J. 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