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 …

Formulated and intensively studied at the beginning of the nineteenth century, the classical
partial differential equations of mathematical physics represent the foundation of our …

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 …

Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff
dimension strictly less than 1 Page 1 © 2021 European Mathematical Society Published by …

We consider the Kolmogorov equation associated with the stochastic Navier–Stokes
equations in 3D, we prove existence of a solution in the strict or mild sense. The method …

We review recent developments in the field of mathematical fluid dynamics which utilize
techniques that go under the umbrella name convex integration. In the hydrodynamical …

In this paper, we consider the 2D incompressible Navier-Stokes equations on the torus. It is
well known that for any L 2 divergence-free initial data, there exists a global smooth solution …

The aim of this book is to provide beginning graduate students who completed the first two
semesters of graduate-level analysis and PDE courses with a first exposure to the …

Asymptotics and stability for global solutions to the Navier-Stokes equations Page 1 ANNA
L E S D E L’INSTITU T FO U RIER ANNALES DE L’INSTITUT FOURIER Isabelle …