In this review article we discuss a number of recent results concerning wild weak solutions of
the incompressible Euler and Navier–Stokes equations. These results build on the …

For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least
one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this …

Abstract For any α\lt1/3, we construct weak solutions to the 3D incompressible Euler
equations in the class C_tC_x^α that have nonempty, compact support in time on R*T^3 and …

We prove that given any $\beta< 1/3$, a time interval $[0, T] $, and given any smooth energy
profile $ e\colon [0, T]\to (0,\infty) $, there exists a weak solution $ v $ of the three …

We survey recent results in the mathematical literature on the equations of incompressible
fluid dynamics, highlighting common themes and how they might contribute to the …

Recently the second and fourth authors developed an iterative scheme for obtaining rough
solutions of the 3D incompressible Euler equations in Hölder spaces. The motivation comes …

We prove that weak solutions of the inviscid SQG equations are not unique, thereby
answering Open Problem 11 of De Lellis and Székelyhidi in 2012. Moreover, we also show …

Abstract For any γ< 1/3, we construct a nontrivial weak solution u to the two-dimensional,
incompressible Euler equations, which has compact support in time and satisfies u∈ C γ (R …

Building upon the techniques introduced in [15], for any θ< 1/10 we construct periodic weak
solutions of the incompressible Euler equations which dissipate the total kinetic energy and …

In this paper, we prove a sharp nonuniqueness result for the incompressible Navier–Stokes
equations in the periodic setting. In any dimension d≥ 2 and given any p< 2, we show the …