An alternative approach to regularity for the Navier–Stokes equations in critical spaces

The regularity criterion of the weak solution to the 3D viscous Boussinesq equations in Besov spaces. Fuyi Xu, Qian Zhang, and

It is well-known that global regularity of the incompressible Navier-Stokes equations is still wide open even in the axisymmetric case with general non-trivial swirl, al- though

In this article we want to study some problems related with the role of the pressure in the partial regularity theory for weak solutions of the Navier–Stokes equations.. Before

Marius Mitrea, Sylvie Monniaux. The regularity of the Stokes operator and the Fujita–Kato approach to the Navier–Stokes initial value problem in Lipschitz domains.. approach to

We prove Theorem 1 in this subsection.. Therefore, if s is large enough, all points along this non degenerate direction satisfy the blow-up exclusion criterion of Proposition 2.3.

Time evolution of each profile, construction of an approximate solution In this section we shall construct an approximate solution to the Navier-Stokes equations by evolving in

Okita: Optimal decay rate for strong solutions in critical spaces to the compressible Navier- Stokes equations, Journal of Differential Equations, 257, 3850–3867 (2014).

In [4]-[6] classes of initial data to the three dimensional, incompressible Navier- Stokes equations were presented, generating a global smooth solution although the norm of the