In this short survey paper, we focus on some new developments in the study of the regularity
or potential singularity formation for solutions of the 3D Navier–Stokes equations. Some of …

This paper addresses several problems associated to local energy solutions (in the sense of
Lemarié-Rieusset) to the Navier-Stokes equations with initial data which is sufficiently small …

We first prove decay estimates and spacetime integral bounds for Stokes flows in amalgam
spaces E qr which connect the classical Lebesgue spaces to the spaces of uniformly locally …

We are concerned with the size of the regular set for weak solutions to the Navier–Stokes
equations. It is shown that if a weighted L 2 norm of initial data is finite, the suitable weak …

We prove an $\epsilon $-regularity criterion for the 3D Navier-Stokes equations in terms of
initial data. It shows that if a scaled local $ L^ 2$ norm of initial data is sufficiently small …

Recently, strong evidence has accumulated that some solutions to the Navier–Stokes
equations in physically meaningful classes are not unique. The primary purpose of this …

Forward self-similar and discretely self-similar weak solutions of the Navier–Stokes
equations are known to exist globally in time for large self-similar and discretely self-similar …

In this paper we develop new methods to obtain regularity criteria for the three-dimensional
Navier–Stokes equations in terms of dynamically restricted endpoint critical norms: the …

In this paper we explore the extent to which discretely self-similar (DSS) solutions to the 3D
Navier-Stokes equations with rough data almost have the same asymptotics as DSS flows …

We establish existence of solutions in a scale of classes weaker than the finite energy Leray
class and stronger than the infinite energy Lemarié-Rieusset class. The new classes are …