2019/03/27 by Feireisl, Eduard, Ghoshal, Shyam Sundar, Jana, Animesh
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1903.11687
The dissipative solutions can be seen as a convenient generalization of the concept of weak solution to the isentropic Euler system. They can be seen as expectations of the Young measures associated to a suitable measure--valued solution of the problem. We show that dissipative solutions coincide with weak solutions starting from the same initial data on condition that: \bf (i) the weak solution enjoys certain Besov regularity; \bf (ii) the symmetric velocity gradient of the weak solution satisfies a one--sided Lipschitz bound.