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The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. <a href="https://mathscinet.ams.org/mathscinet/search/journal/profile?groupId=3285" target="new">Subscribers to MathSciNet</a> may click through for more detailed information. </div> </p> </section> </div> </header> <main> <section class="row"> <nav class="col-md-3">  <nav class="journals-list-group"> <script type="text/javascript" src="/journals/javascript/tran_nav.js"></script> <a href="/journals/journals"><i class="fa-sharp fa-solid fa-house"></i> Journals Home</a> <a href="/epubsearch">eContent Search</a> <a href="/abouttran" class="">About Transactions of the American Mathematical Society</a> <a href="/tranedit" class="">Editorial Board</a> <a href="/tran/transubmit.html" class="">Author and Submission Information</a> <a href="/policies/policies" class="" target="_blank">Journal Policies</a> <a href="/subscriberinfo" class="" target="_blank">Subscription Information</a> <a href="/jemail" class="" target="_blank"> Journal Email Notifications</a> <hr> <a href="/pairing/pair_my_device.html"><i class="fa fa-globe" aria-hidden="true"></i> Remote Access</a> </nav> </nav> <article class="col-md-9"> <section>   <div class="row">  <ul class="nav nav-tabs"> <li role="presentation" class=""> <script type="text/javascript" src="/journals/javascript/tran_nav.js"></script> <a href="javascript: goto_most_recent_tran()" aria-controls="currissue" role="tab"> Current volume </a> </li> <li role="presentation" class="">  <a href="/cgi-bin/mstrack/accepted_papers/tran?active=press" aria-controls="press" role="tab">Articles in press </a> </li> <li role="presentation" class=""> <a href="/journals/tran/0000-000-00?active=recent"> Recently published</a> </li> <li role="presentation" class=""> <a href="/journals/tran/all_issues.html?active=allissues"> All issues : 1900 – Present </a> </li> </ul> <script src="/js/abstracts/ajaxcall.js"></script> </div> <p> </p> <style> #navCell { display: none;} </style> <script src="/journals/javascript/references.js" type="text/javascript"></script> <script async src="/js/mj.js"></script> <article class="col-md-12"> <header> <h2>Solutions of Navier–Stokes–Maxwell systems in large energy spaces<br> <small>HTML articles powered by AMS MathViewer <a href="/AMSMathViewer"><i class="fa fa-info-circle" aria-label="about MathViewer"></i></a></small></h2> <dl> <dd>by <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Arsenio%2C%20Diogo">Diogo Arsénio</a> and <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?mrauthid=617258">Isabelle Gallagher</a> <span class="pull-right"> <a href="S0002-9947-2020-08000-3.pdf"><small>PDF</small></a> </span> </dd> <dd>Trans. Amer. Math. Soc. <strong>373</strong> (2020), 3853-3884 <span class="pull-right"><a href="https://www.copyright.com/openurl.do?issn=1088-6850&WT.mc.it=American%20Mathematical%20Society" target="_blank">Request permission</a></span> </dd> </dl> </header> <section id="Abstract"> <h2>Abstract:</h2> <p>Large weak solutions to Navier–Stokes–Maxwell systems are not known to exist in their corresponding energy space in full generality. Here, we mainly focus on the three-dimensional setting of a classical incompressible Navier–Stokes–Maxwell system and—in an effort to build solutions in the largest possible functional spaces—prove that global solutions exist under the assumption that the initial velocity and electromagnetic fields have finite energy, and that the initial electromagnetic field is small in $\dot H^s\left ({\mathbb R}^3\right )$ with $s\in \left [\frac 12,\frac 32\right )$. We also apply our method to improve known results in two dimensions by providing uniform estimates as the speed of light tends to infinity.</p> <p>The method of proof relies on refined energy estimates and a Grönwall-like argument, along with a new maximal estimate on the heat flow in Besov spaces. The latter parabolic estimate allows us to bypass the use of the so-called Chemin–Lerner spaces altogether, which is crucial and could be of independent interest.</p> </section> <section id="references"> <details> <summary>References</summary> <ul> <li><a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Arsenio%2C%20Diogo">Diogo Arsénio</a>, <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Ibrahim%2C%20Slim">Slim Ibrahim</a>, and <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Masmoudi%2C%20Nader">Nader Masmoudi</a>, <em>A derivation of the magnetohydrodynamic system from Navier-Stokes-Maxwell systems</em>, Arch. Ration. Mech. 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(4) <strong>146</strong> (1987), 65–96. <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=916688">MR <strong>916688</strong></a>, DOI <a href="https://doi.org/10.1007/BF01762360">10.1007/BF01762360</a></li> </ul> </details> </section> <section id="similar"> <details> <summary>Similar Articles</summary> <ul> <li> Retrieve articles in <em>Transactions of the American Mathematical Society</em> with MSC (2010): <a href="/joursearch/servlet/DoSearch?f1=msc&v1=35Q35&jrnl=one&onejrnl=tran">35Q35</a> </li> <li> Retrieve articles in all journals with MSC (2010): <a href="/joursearch/servlet/DoSearch?f1=msc&v1=35Q35">35Q35</a> </ul> </details> </section> <section id="additionalinformation"> <details> <summary>Additional Information</summary> <ul> <li><strong>Diogo Arsénio</strong></li><li>Affiliation: Department of Mathematics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates</li> <li>Email: diogo.arsenio@nyu.edu</li> <li><strong>Isabelle Gallagher</strong></li><li>Affiliation: DMA, École normale supérieure, CNRS, PSL Research University, 75005 Paris; and UFR de mathématiques, Université Paris-Diderot, Sorbonne Paris-Cité, 75013 Paris, France</li> <li>MR Author ID: <a href='https://mathscinet.ams.org/mathscinet/search/authors.html?mrauthid=617258'>617258</a></li><li>Email: gallagher@math.ens.fr</li> <li>Received by editor(s): November 4, 2018</li> <li>Published electronically: March 9, 2020</li> <li>© Copyright 2020 American Mathematical Society</li> <li>Journal: Trans. Amer. Math. Soc. <strong>373</strong> (2020), 3853-3884 </li> <li>MSC (2010): Primary 35Q35 <li>DOI: https://doi.org/10.1090/tran/8000</li> <li>MathSciNet review: <a href = "https://mathscinet.ams.org/mathscinet-getitem?mr=4105512">4105512</a></li> </ul> </details> </section> </article> </section> </article> </section> </main> </div>   <hr class="mx-auto"> <footer id="pagefooter" class="text-center"> <div class="container text-center"> <div class="row">  <div class="col-12 mb-1"> <p> American Mathematical Society · <a href="https://goo.gl/maps/ZvJdkQEC79p" title="Google map 201 Charles Street Providence, Rhode Island" aria-label="Google map to AMS headquarters"> 201 Charles Street Providence, Rhode Island 02904-2213 </a> · <a href="/reach" aria-label="Contact Us">Contact Us</a> </p> </div>  <script src="https://kit.fontawesome.com/2ad6d7fbd6.js" crossorigin="anonymous" defer></script>  <nav class="col-12 mb-1" aria-label="Social media links"> <ul class="list-inline"> <li class="list-inline-item"> <a href="https://www.facebook.com/amermathsoc" class="link-dark" title="Follow us on Facebook" aria-label="View the AMS on Facebook"> <i class="fa-brands fa-facebook-f" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://bsky.app/profile/amermathsoc.bsky.social" class="link-dark" title="Follow us on Bluesky" aria-label="View the AMS on Bluesky"> <i class="fa-brands fa-bluesky"></i></a></li> <li class="list-inline-item"> <a href="https://twitter.com/amermathsoc" class="link-dark" title="Follow us on X" aria-label="View the AMS on X"> <i class="fa-brands fa-x-twitter" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.linkedin.com/company/51001" class="link-dark" title="Follow us on LinkedIn" aria-label="View the AMS on LinkedIn"> <i class="fa-brands fa-linkedin-in" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.instagram.com/amermathsoc" class="link-dark" title="Follow us on Instagram" aria-label="View the AMS on Instagram"> <i class="fa-brands fa-instagram" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.youtube.com/amermathsoc" class="link-dark" title="Follow us on YouTube" aria-label="View the AMS on YouTube"> <i class="fa-brands fa-youtube" aria-hidden="true"></i></a></li> </ul> </nav>  <div class="col-12"> <p><small> © <a href="/copyright" aria-label="Copyright policy">Copyright</a> <span id="copyYear">2024</span> American Mathematical Society · <a href="/privacy" aria-label="Privacy statement">View Our Privacy Statement</a> · <a href="/tou" aria-label="Terms of use">Terms of Use</a> · <a href="/accessibility" aria-label="Accessibility policy">Accessibility and AMS Online Content</a> </small></p> <p><small> AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and service marks of the American Mathematical Society and registered in the U.S. Patent and Trademark Office. </small></p> </div> </div> </div> <script> // Dynamically update the copyright year document.getElementById('copyYear').textContent = new Date().getFullYear(); </script> </footer>