Document Zbl 1534.35456

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(2024)</a>. </div> <div class="abstract">Summary: In this article, we study a mathematical system modelling the dynamic of the collective behaviour of oxygen-driven swimming bacteria in an aquatic fluid flowing in a two dimensional bounded domain under stochastic perturbation. This model can be seen as a stochastic version of Chemotaxis-Navier-Stokes model. We prove the existence of a unique (probabilistic) strong solution. In addition, we establish some properties of the strong solution. More precisely, we prove that the unique solution is positive and satisfies the mass conservation property and an energy inequality.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7812483">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R60" title="MSC2020">35R60</a> </td> <td class="space"> PDEs with randomness, stochastic partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35K51" title="MSC2020">35K51</a> </td> <td class="space"> Initial-boundary value problems for second-order parabolic systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35K59" title="MSC2020">35K59</a> </td> <td class="space"> Quasilinear parabolic equations </td> </tr><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%3A60H15" title="MSC2020">60H15</a> </td> <td class="space"> Stochastic partial differential equations (aspects of stochastic analysis) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M35" title="MSC2020">76M35</a> </td> <td class="space"> Stochastic analysis applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A86A05" title="MSC2020">86A05</a> </td> <td class="space"> Hydrology, hydrography, oceanography </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C17" title="MSC2020">92C17</a> </td> <td class="space"> Cell movement (chemotaxis, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ANavier-Stokes+system">Navier-Stokes system</a>; <a href="/?q=ut%3Achemotaxis">chemotaxis</a>; <a href="/?q=ut%3Astochastic">stochastic</a>; <a href="/?q=ut%3Aprobabilistic+weak+solution">probabilistic weak solution</a>; <a href="/?q=ut%3Astrong+solution">strong solution</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 1534.35456" data-ciurl="/ci/07812483" data-biburl="/bibtex/07812483.bib" data-amsurl="/amsrefs/07812483.bib" data-xmlurl="/xml/07812483.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07812483.pdf" title="Zbl 1534.35456 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.spa.2023.104274" aria-label="DOI for “On the existence and uniqueness of solution to a stochastic chemotaxis-Navier-Stokes model”" title="10.1016/j.spa.2023.104274">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2301.00654"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">Adams, R. 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