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math.AP2021★ 6 cited
Instability and nonuniqueness for the Euler equations in vorticity form, after M. Vishik
Dallas Albritton, Elia Brué, Maria Colombo +4
In this expository work, we present Vishik's theorem on non-unique weak solutions to the two-dimensional Euler equations on the whole space, \[ \partial_t ω+ u \cdot \nabla ω= f \,…
math.AP2021★ 10 cited
On Non-uniqueness of continuous entropy solutions to the isentropic compressible Euler equations
Vikram Giri, Hyunju Kwon
We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density aw…
math.AP2021
Non-uniqueness of integral curves for autonomous Hamiltonian vector fields
Vikram Giri, Massimo Sorella
In this work we prove the existence of an autonomous Hamiltonian vector field in W^{1,r}(T^d;R^d) with r< d-1and d>=4 for which the associated transport equation has non-unique pos…