TY - JOUR
T1 - Inviscid limit for the compressible Euler system with non-local interactions
AU - Březina, Jan
AU - Mácha, Václav
N1 - Funding Information:
The research of V. M. has been supported by the grant NRF-20151009350.
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/9/15
Y1 - 2019/9/15
N2 - The collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals. This system can be viewed as a generalization of the compressible Euler equations with all of its unpleasant consequences, e.g., the non-uniqueness of solutions. In this paper, we analyze the equations describing a viscous approximation of a generalized compressible Euler system and we show that its dissipative measure-valued solutions tend to a strong solution of the Euler system as viscosity tends to zero, provided the strong solution exists.
AB - The collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals. This system can be viewed as a generalization of the compressible Euler equations with all of its unpleasant consequences, e.g., the non-uniqueness of solutions. In this paper, we analyze the equations describing a viscous approximation of a generalized compressible Euler system and we show that its dissipative measure-valued solutions tend to a strong solution of the Euler system as viscosity tends to zero, provided the strong solution exists.
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U2 - 10.1016/j.jde.2019.05.012
DO - 10.1016/j.jde.2019.05.012
M3 - Article
AN - SCOPUS:85065446221
SN - 0022-0396
VL - 267
SP - 4410
EP - 4428
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 7
ER -