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math.AP2021★ 13 cited
Non-uniqueness of Leray solutions of the forced Navier-Stokes equations
Dallas Albritton, Elia Brué, Maria Colombo
In the seminal work [39], Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. We exhibit two distinct Leray solutions with…
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
Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space
Elia Brué, Maria Colombo
For the two dimensional Euler equations, a classical result by Yudovich states that solutions are unique in the class of bounded vorticity; it is a celebrated open problem whether…