13 citations · 19 across the 8 of their papers we have counts for
8 papers
Flexibility for the SQG Equation with an Active Scalar
Elia Bruè, Rui Jin, Quoc-Hung Nguyen
We develop a new convex-integration scheme, inspired by \cite{BCK26}, for the inviscid surface quasi-geostrophic equation on the two-dimensional torus. For the explicit, nonoptimiz…
Regularity estimates in transport equations via heat flow and quantitative differentiation
Elia Brué, Maria Colombo, Guido De Philippis +1
The purpose of this note is twofold. First, we prove quantitative estimates for the Ambrosio-Trevisan commutator which implies propagation of logarithmic Sobolev regularity. Second…
Topology of two-dimensional collapsed spaces with lower Ricci bounds
Elia Bruè, Qin Deng
We prove that collapsed metric measure spaces with Ricci curvature bounded below and essential dimension two are topological surfaces, possibly with boundary.
Lyapunov exponents, entropy and mixing for DiPerna-Lions flows
Elia Brué, Maria Colombo, Carl Johan Peter Johansson
The main goal of this work is to establish an asymptotic form of Bressan's mixing conjecture. To this end, we develop an ergodic-theoretic framework for incompressible DiPerna-Lion…
Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations
Elia Brué, Rui Jin, Yachun Li +1
This paper concerns the forced stochastic Navier-Stokes equation driven by additive noise in the three dimensional Euclidean space. By constructing an appropriate forcing term, we…
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…
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 \,…
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…