Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis
The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize …

It is not known whether the three-dimensional (3D) incompressible Navier-Stokes equations
possess unique smooth (continuously differentiable) solutions at high Reynolds numbers …

Since the early part of the 20th century, it has been understood that the description of nature
at the subatomic scale requires quantum mechanics. In quantum mechanics, the position …

We consider the regularity criteria for the incompressible Navier–Stokes equations
connected with one velocity component. Based on the method from Cao and Titi (2008 …

The overall performance of lithium-ion battery is determined by the innovation of material
and structure of the battery, while it is significantly dependent on the progress of the …

Grzegorz Łukaszewicz Piotr Kalita An Introduction with Applications Page 1 Advances in
Mechanics and Mathematics 34 Grzegorz Łukaszewicz Piotr Kalita Navier– Stokes …

We establish sufficient conditions for the regularity of solutions of the Navier–Stokes system
based on conditions on one component of the velocity. The first result states that if, where …

We improve the regularity criterion for the incompressible Navier–Stokes equations in the
full three-dimensional space involving the gradient of one velocity component. The method …

In this paper, we establish two new regularity criteria for the 3D incompressible MHD
equations involving partial components of the velocity and magnetic fields. It is proved that if …

In this paper we consider the three–dimensional Navier–Stokes equations subject to
periodic boundary conditions or in the whole space. We provide sufficient conditions, in …