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UID:news1313@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20220320T140750
DTSTART;TZID=Europe/Zurich:20220323T141500
SUMMARY:Seminar Analysis and Mathematical Physics: Dr. Raphael Winter (ENS 
 Lyon)
DESCRIPTION:Following the pioneering work of Lanford\, a rigorous theory ha
 s been developed for the validation of the Boltzmann equation in the low-d
 ensity Grad scaling. In the physics literature\, an important issue are th
 e corrections to the equation for small but positive volume fraction. The 
 first order correction to the Boltzmann equation is conjectured to be give
 n by the so-called Choh-Uhlenbeck equation\, which is of the form\\r\\n∂
 tfϵ=Qϵ\,BE(fϵ\,fϵ)+ϵQϵ\,CU(fϵ\,fϵ\,fϵ).\\r\\n Here Qϵ\,BE is the
  Boltzmann-Enskog operator\, and the Choh-Uhlenbeck operator Qϵ\,CU is an
  explicit cubic operator. This operator accounts for the formation of dyna
 mic microscopic correlations between three particles. In this work\, we pr
 ove rigorously that the Choh-Uhlenbeck equation gives the first order corr
 ection to the Boltzmann equation in the Grad-scaling. This is a joint work
  with Sergio Simonella.
X-ALT-DESC:<p>Following the pioneering work of Lanford\, a rigorous theory 
 has been developed for the validation of the Boltzmann equation in the low
 -density Grad scaling. In the physics literature\, an important issue are 
 the corrections to the equation for small but positive volume fraction. Th
 e first order correction to the Boltzmann equation is conjectured to be gi
 ven by the so-called Choh-Uhlenbeck equation\, which is of the form</p>\n<
 p><span id="MathJax-Element-1-Frame">∂<span id="MJXc-Node-5">t</span>f<s
 pan id="MJXc-Node-8">ϵ</span>=Q<span id="MJXc-Node-12">ϵ\,BE</span>(f<sp
 an id="MJXc-Node-21">ϵ</span>\,f<span id="MJXc-Node-25">ϵ</span>)+ϵQ<sp
 an id="MJXc-Node-31">ϵ\,CU</span>(f<span id="MJXc-Node-40">ϵ</span>\,f<s
 pan id="MJXc-Node-44">ϵ</span>\,f<span id="MJXc-Node-48">ϵ</span>).</spa
 n></p>\n<p><br /> Here <span id="MathJax-Element-2-Frame">Q<span id="MJXc-
 Node-55">ϵ\,BE</span></span> is the Boltzmann-Enskog operator\, and the C
 hoh-Uhlenbeck operator <span id="MathJax-Element-3-Frame">Q<span id="MJXc-
 Node-65">ϵ\,CU </span></span>is an explicit cubic operator. This operator
  accounts for the formation of dynamic microscopic correlations between th
 ree particles. In this work\, we prove rigorously that the Choh-Uhlenbeck 
 equation gives the first order correction to the Boltzmann equation in the
  Grad-scaling. This is a joint work with Sergio Simonella.</p>
DTEND;TZID=Europe/Zurich:20220323T160000
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