Document Zbl 1370.76025

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B.</a></div> <h2 class="title"> <strong>A velocity minimum in a potential fluid flow.</strong> <i>(English. Russian original)</i> <a class="label nowrap" href="/1370.76025">Zbl 1370.76025</a> </h2> <div class="source"> <a href="/serials/79" title="Journal Profile">Fluid Dyn.</a> <a href="/?q=in%3A368915" title="Articles in this Issue">52, No. 3, 345-350 (2017)</a>; translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2017, No. 3, 12-17 (2017). </div> <div class="abstract">Summary: An example of three-dimensional potential flow of an inviscid incompressible fluid is presented, in which the point of a strict non-zero local minimum of velocity is an internal point of the flow. This proves the impossibility to extend to a three-dimensional flow the two-dimensional velocity minimum principle, according to which in plane potential flows of incompressible fluid the flow velocity cannot have a local non-zero minimum at an internal point.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76B99" title="MSC2020">76B99</a> </td> <td class="space"> Incompressible inviscid fluids </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aincompressible+fluid">incompressible fluid</a>; <a href="/?q=ut%3Avelocity+minimum+principle">velocity minimum principle</a>; <a href="/?q=ut%3Apotential+flow">potential flow</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 1370.76025" data-ciurl="/ci/06774779" data-biburl="/bibtex/06774779.bib" data-amsurl="/amsrefs/06774779.bib" data-xmlurl="/xml/06774779.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06774779.pdf" title="Zbl 1370.76025 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/10.1134/S0015462817030024" aria-label="DOI for “A velocity minimum in a potential fluid flow”" title="10.1134/S0015462817030024">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">L. I. Sedov, A Course in Continuum Mechanics. V. 2 (Wolters-Noordhoff, Groningen, 1971). · <a href="/0308.73005" class="nowrap">Zbl 0308.73005</a></td> </tr><tr> <td>[2]</td> <td class="space">G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1970). · <a href="/0152.44402" class="nowrap">Zbl 0152.44402</a></td> </tr><tr> <td>[3]</td> <td class="space">J. Serrin, Mathematical Principles of Classical Fluid Mechanics (Springer-Verlag, Berlin, 1959). · <a href="https://doi.org/10.1007/978-3-642-45914-6_2" class="nowrap">doi:10.1007/978-3-642-45914-6_2</a></td> </tr><tr> <td>[4]</td> <td class="space">V. N. Golubkin, V. P. Kovalev, and G. B. Sizykh, “A Pressure Maximum Principle in Plane Flows of Inviscid Incompressible Fluid,” Uchenye Zap. TsAGI 47 (6), 28-36 (2016).</td> </tr><tr> <td>[5]</td> <td class="space">A. N. Burmistrov, V. P. Kovalev, and G. B. Sizykh, “A Maximum Principle for the Solution of an Equation of Elliptic Type with Unbounded Coefficients,” Trydy MIPT 6 (4), 97-102 (2014).</td> </tr><tr> <td>[6]</td> <td class="space">L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics (JohnWiley and Sons, New York, 1958). · <a href="/0083.20501" class="nowrap">Zbl 0083.20501</a></td> </tr><tr> <td>[7]</td> <td class="space">M. Shiffman, “On the Existence of Subsonic Flows of a Compressible Fluid” J. Ration. Mech. Anal. 1, 605-652 (1952). · <a href="/0048.19301" class="nowrap">Zbl 0048.19301</a></td> </tr><tr> <td>[8]</td> <td class="space">D. Gilbarg and M. Shiffman, “On Bodies Achieving Extreme Value of the Critical Mach Number. I.” J. Rotion. Mech. Anal. 3 (4), 209-230 (1954). · <a href="/0055.18801" class="nowrap">Zbl 0055.18801</a></td> </tr><tr> <td>[9]</td> <td class="space">G. B. Sizykh, “The Criterion of the Presence of a Stagnation Point in a Plane Irrotational Flow of Inviscid Gas,” Trudy MIPT 7 (2), 108-112 (2015).</td> </tr><tr> <td>[10]</td> <td class="space">A. N. Kraiko, “Plane and Axisymmetric Configurations Immersed in Flow with Maximum Critical Mach Number,” Prikl. Matem. Mekh. 51 (6), 941-950.</td> </tr><tr> <td>[11]</td> <td class="space">M. A. Brutyan and S. V. Lyapunov, “Optimization of the Shape of Symmetric Plane Bodies with the Aim to Increase the Critical Mach Number,” Uchen. Zap. TsAGI 12 (5), 10-22 (1981).</td> </tr><tr> <td>[12]</td> <td class="space">V. V. Vyshinskii and E. N. Kuznetsov, “Investigation of Head Parts of Bodies of Revolution with the Ryabushinskii Generatrix,” Uchen Zap. TsAGI 23 (1), 3-8 (1992).</td> </tr><tr> <td>[13]</td> <td class="space">L. G. Loitsyanskii, Mechanics of Liquids and Gases, (Pergamon, Oxford, 1966). · <a href="/0247.76001" class="nowrap">Zbl 0247.76001</a></td> </tr><tr> <td>[14]</td> <td class="space">L. Rosenhead, “The Formation of Vortices from a Surface of Discontinuity,” Proc. Roy. Soc. London A 134, 170-192 (1931). · <a href="/0003.08401" class="nowrap">Zbl 0003.08401</a> · <a href="https://doi.org/10.1098/rspa.1931.0189" class="nowrap">doi:10.1098/rspa.1931.0189</a></td> </tr><tr> <td>[15]</td> <td class="space">S. M. Belotserkovskii and M. I. Nisht, Separated and Non-Separated Flow of Inviscid Gas around Slender Wings [in Russian] (Nauka, Moscow, 1972).</td> </tr><tr> <td>[16]</td> <td class="space">G.-H. Cottet and P. Koumotsakos, VortexMethods: Theory and Practice (CambridgeUniversity Press, Cambridge, 2000).</td> </tr><tr> <td>[17]</td> <td class="space">V. A. Gutnikov, I. K. Lifanov, and A. V. Setukha, “Simulation of Aerodynamics of Buildings and Structures by Means of the Closed Vortex Loop Method,” Fluid Dynamics 41 (4), 555-567 (2006). · <a href="/1200.76137" class="nowrap">Zbl 1200.76137</a> · <a href="https://doi.org/10.1007/s10697-006-0073-4" class="nowrap">doi:10.1007/s10697-006-0073-4</a></td> </tr><tr> <td>[18]</td> <td class="space">M. A. Lavrent’ev and B. V. Shabat Methods of Functions of a Complex Variable [in Russian] (Nauka, Moscow, 1973). · <a href="/0633.30001" class="nowrap">Zbl 0633.30001</a></td> </tr><tr> <td>[19]</td> <td class="space">G. Stokes, “On the Steady Motion of Incompressible Fluids,” Transac. Cambridge Phil. Soc. 7, 439-459 (1842).</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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