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UID:news1514@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20230516T094922
DTSTART;TZID=Europe/Zurich:20230524T141500
SUMMARY:Seminar Analysis and Mathematical Physics: Thérèse Moerschell (EP
 FL)
DESCRIPTION:The advection-diffusion equation is known to have unique soluti
 ons for any vector field that is L^2 in time and in space. But what happen
 s when we have slightly less than square integrability? In this talk we wi
 ll explore two examples of vector fields in L^p(0\,T\;L^q(\\T^d)) made of 
 shear flows that prove the non-uniqueness of solutions whenever we have p<
 2 or q<2. We will first show that they give different solutions to the adv
 ection equation and then use the Feynman-Kac formula to show that diffusio
 n has little effect if our parameters are well-tuned. This is part of my M
 aster's thesis\, supervised by Massimo Sorella and Maria Colombo.
X-ALT-DESC:<p>The advection-diffusion equation is known to have unique solu
 tions for any vector field that is L^2 in time and in space. But what happ
 ens when we have slightly less than square integrability? In this talk we 
 will explore two examples of vector fields in L^p(0\,T\;L^q(\\T^d)) made o
 f shear flows that prove the non-uniqueness of solutions whenever we have 
 p&lt\;2 or q&lt\;2. We will first show that they give different solutions 
 to the advection equation and then use the Feynman-Kac formula to show tha
 t diffusion has little effect if our parameters are well-tuned.<br /> This
  is part of my Master's thesis\, supervised by Massimo Sorella and Maria C
 olombo.</p>
DTEND;TZID=Europe/Zurich:20230524T160000
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