2015/02/22 by Eduard Feireisl, A Swierczewska-Gwiazda, Piotr Gwiazda +4 · 1 citation
Engineering · Mathematics · Medicine · #Applied mathematics #Biological system #Biology #Bounded function #Dimension (graph theory) #Dissipative system #Euler equations #Euler system #Euler's formula #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Navier-Stokes equation solutions #Nonlinear system #Physics #Pure mathematics #Stability and Controllability of Differential Equations #Uniqueness #Weak solution #math.AP #msc:35L30 #msc:76T25
paper · pdf · open access · doi:10.1112/jlms.12027
published in Journal of the London Mathematical Society 95(3), 705-724 (Wiley) · 17 pages
arxiv created 2015/02/22 · openalex publication_date 2017/02/14 · arxiv updated 2017/06/14 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05
We consider several modifications of the Euler system of fluid dynamics, including its pressureless variant driven by non-local interaction repulsive–attractive and alignment forces in the space dimension N = 2 , 3 . These models arise in the study of self-organization in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global-in-time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality). We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak–strong uniqueness principle for the pressure-driven Euler system with non-local interaction terms as well as for the pressureless system with Newtonian interaction.