On the failure of the chain rule for the divergence of Sobolev vector fields

A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus

(2022) Tomasz Cieślak et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves

(2021) Elia Brué et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Non Uniqueness of Power-Law Flows

(2021) Jan Burczak et al.   COMMUNICATIONS IN MATHEMATICAL PHYSICS

Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

(2021) Tristan Buckmaster et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Convex integration solutions to the transport equation with full dimensional concentration

(2020) Stefano Modena et al.   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

Stationary Solutions and Nonuniqueness of Weak Solutions for the Navier–Stokes Equations in High Dimensions

(2019) Xiaoyutao Luo   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Non-renormalized solutions to the continuity equation

(2019) Stefano Modena et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

A uniqueness result for the decomposition of vector fields in \mathbb {R}^d R d

(2019) Stefano Bianchini et al.   INVENTIONES MATHEMATICAE

Onsager's Conjecture for Admissible Weak Solutions

(2018) Tristan Buckmaster et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Steady Nearly Incompressible Vector Fields in Two-Dimension: Chain Rule and Renormalization

(2016) S. Bianchini et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Dissipative Euler flows and Onsager's conjecture

(2014) Camillo De Lellis et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Dissipative continuous Euler flows

(2012) Camillo De Lellis et al.   INVENTIONES MATHEMATICAE

The Euler equations as a differential inclusion

(2010) Camillo De Lellis et al.   ANNALS OF MATHEMATICS