Weak solutions for Euler systems with non-local interactions
File(s)
Author(s)
Carrillo de la Plata, J
Feireisl, E
Gwiazda, P
Swierczewska-Gwiazda, A
Type
Journal Article
Abstract
We consider several modi cations of the Euler system of uid 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-organisation in collective behavior modeling of animals and
crowds. We adapt the method of convex integration to show the existence of in nitely 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 in nitely 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.
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-organisation in collective behavior modeling of animals and
crowds. We adapt the method of convex integration to show the existence of in nitely 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 in nitely 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.
Date Issued
2017-02-14
Date Acceptance
2016-12-20
Citation
Journal of the London Mathematical Society - Second Series, 2017, 95 (3), pp.705-724
ISSN
0024-6107
Publisher
London Mathematical Society
Start Page
705
End Page
724
Journal / Book Title
Journal of the London Mathematical Society - Second Series
Volume
95
Issue
3
Copyright Statement
© 2017 London Mathematical Society
Sponsor
The Royal Society
Grant Number
WM120001
Subjects
Science & Technology
Physical Sciences
Mathematics
MEASURE-VALUED SOLUTIONS
DRIVEN AVALANCHE FLOW
STRONG UNIQUENESS
FLOCKING DYNAMICS
MODEL
PARTICLE
EQUATIONS
LIMIT
BEHAVIOR
MOTION
0101 Pure Mathematics
General Mathematics
Publication Status
Published