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Seminar on partial differential equations

Relaxation limit of hydrodynamic models

Aneta Wróblewska-Kamińska
Institute of Mathematics, Polish Academy of Sciences

 

Tuesday, 7. March 2023 - 9:00 to 10:00

in IM, rear building, ground floor and on Zoom
Link:        https://cesnet.zoom.us/j/91015942151?pwd=dlF4ekVIUGFBRzdIVVUzbUp3MFNQdz09
Meeting ID:    910 1594 2151
Passcode:    051433

The recording of the lecture is available at: https://download.math.cas.cz/media/seminars/PDE/Necas_PDE_Seminar,_March_7,_2023.mp4

We will show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method. We plan to discuss the assumptions on the confinement and interaction potentials depending on the relative energy of the free energy functional allowing for this relaxation limit to hold. We will deal with weak solutions for the nonlocal compressible Euler-type systems and strong solutions for the limiting aggregation-diffusion equations. Finally, we will mention how to show the existence of weak solutions to the nonlocal compressible Euler-type systems satisfying the needed properties for completeness sake.
This is a joint result with Jose Carrillo and Yingping Peng.