<div dir="ltr"><div>Seminari di Matematica Applicata, Dipartimento di Matematica &quot;F. Casorati&quot; e Istituto del CNR IMATI &quot;E. Magenes&quot; di Pavia.<br><br>Martedì 4 Febbraio 2025, alle ore 15 precise, presso l&#39;aula Beltrami del Dipartimento di Matematica,<br><br><h4 style="padding:0px;margin:0px 0px 10px;clear:none;color:rgb(23,28,36);font-weight:300;font-stretch:normal;font-size:24px;line-height:1.2;font-family:Montserrat,-apple-system,system-ui,&quot;Segoe UI&quot;,Roboto,sans-serif;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal;box-sizing:border-box;text-decoration-style:initial;text-decoration-color:initial">Gianluca Crippa (Università di Basilea)</h4><h4 style="padding:0px;margin:0px 0px 10px;clear:none;color:rgb(23,28,36);font-weight:300;font-stretch:normal;line-height:1.2;font-family:Montserrat,-apple-system,BlinkMacSystemFont,&quot;Segoe UI&quot;,Roboto,sans-serif;box-sizing:border-box"><span style="color:rgb(34,34,34);font-family:Arial,Helvetica,sans-serif"><br></span></h4><h4 style="padding:0px;margin:0px 0px 10px;clear:none;color:rgb(23,28,36);font-weight:300;font-stretch:normal;line-height:1.2;font-family:Montserrat,-apple-system,BlinkMacSystemFont,&quot;Segoe UI&quot;,Roboto,sans-serif;box-sizing:border-box"><span style="color:rgb(34,34,34);font-family:Arial,Helvetica,sans-serif">terrà un seminario dal titolo:</span></h4><div><br></div><h3 style="padding:0px;margin:5px 0px 8px;clear:none;color:rgb(23,28,36);font-weight:300;font-stretch:normal;font-size:28px;line-height:1.2;font-family:Montserrat,-apple-system,system-ui,&quot;Segoe UI&quot;,Roboto,sans-serif;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal;box-sizing:border-box;text-decoration-style:initial;text-decoration-color:initial">Weak, renormalized, and vanishing-viscosity solutions of the two-dimensional Euler equations.</h3></div><div><br></div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px">Abstract. </span></div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px;font-variant-ligatures:normal;text-decoration-style:initial;text-decoration-color:initial">Let us consider the Euler equations modeling the behavior of an incompressible, homogeneous, inviscid fluid. In the two-dimensional case, the Euler equations can be written in vorticity form as a continuity equation, in which the advecting velocity depends on the vorticity through an integral operator. In my talk, I will introduce several notions of weak solutions for the two-dimensional Euler equations in vorticity form: weak solutions, renormalized solutions, and vanishing-viscosity solutions. Relying on the linear theory for continuity equations with Sobolev velocity field by DiPerna and Lions, I will show that in the subcritical case weak solutions do not exhibit anomalies. In the supercritical case, I will show by means of a duality approach that the same holds for vanishing-viscosity solutions. This has some connections with the two-dimensional theory of turbulence of Kraichnan and Batchelor.</span><br></div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px;font-variant-ligatures:normal;text-decoration-style:initial;text-decoration-color:initial">-----------------------------------------</span></div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px;font-variant-ligatures:normal;text-decoration-style:initial;text-decoration-color:initial"><a href="https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/">https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/</a><br></span></div><div><span style="color:rgb(61,61,61);font-family:Roboto,sans-serif;font-size:15px;font-variant-ligatures:normal;text-decoration-style:initial;text-decoration-color:initial"><br></span></div></div>