On the sticky particle solutions to the multi-dimensional pressureless Euler equations

Abstract: Abstract: In this talk we consider the multi-dimensional pressureless Eulersystem and we tackle the problem of existence and uniqueness of sticky particlesolutions for general measure-type initial data. Although explicit counterexam-ples to both existence and uniqueness are known, the problem of whether onecan still find sticky particle solutions for a large set of data and of how one canselect them was up to our knowledge still completely open. In this talk we provethat for a comeager set of initial data in the weak topology the pressureless Eu-ler system admits a unique sticky particle solution given by a free flow wheretrajectories are disjoint straight lines. Indeed, such an existence and unique-ness result holds for a broader class of solutions decreasing their kinetic energy,which we call dissipative solutions, and which turns out to be the compact weakclosure of the classical sticky particle solutions. Therefore any scheme for whichthe energy is l.s.c. and is dissipated will converge, for a comeager set of data,to our solution, i.e. the free flow

analysis of PDEsdynamical systemsfunctional analysisoptimization and controlspectral theory

Audience: advanced learners

Webinar on PDE and related areas

Series comments: The webinar is organised jointly from IIT-Kanpur, TIFR-CAM,Bangalore, IISER-Pune and IISER-Kolkata.

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