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Non-renormalized solutions to the continuity equation

2019; Springer Science+Business Media; Volume: 58; Issue: 6 Linguagem: Inglês

10.1007/s00526-019-1651-8

1432-0835

Stefano Modena, László Székelyhidi,

Stability and Controllability of Differential Equations

Abstract We show that there are continuous, $$W^{1,p}$$ W 1 , p ( $$p<d-1$$ p < d - 1 ), incompressible vector fields for which uniqueness of solutions to the continuity equation fails.