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In this remark, we consider regularity criterion for weak solutions to the 3d incompressible Navier–Stokes equations via pressure. It is proved that if the corressponding pressure P satisfies ∇ h ˜ P ∈ L β (0 , T ; L p (R x 1 ; L q (R x 2 ; L r (R x 3)))) with 2 β + 1 p + 1 q + 1 r = 3 , 6 5 < p , q , r ≤ 3 and 2 − (1 p + 1 q + 1 r) ≥ 0 , then the weak solution remains smooth on (0 , T ] . Here, ∇ h ˜ = (0 , ∂ 2 , ∂ 3) . [ABSTRACT FROM AUTHOR]

A one-component regularity criterion for the non-resistive axially symmetric Hall-MHD system is given in this paper. More precisely, we show that strong solutions to a family of axially symmetric initial data, whose velocity and current density have trivial swirl components, could be smoothly extended beyond a possible blow-up time T ∗ if and only if the swirl component of the magnetic field h θ satisfies a Beale-Kato-Majda-type criterion. See (1.5) below. This criterion is not trivial even if the velocity field vanishes since the quantity h θ r satisfies a partial Burgers' equation in this situation. [ABSTRACT FROM AUTHOR]

In this paper we establish a regularity criterion for the 2D full compressible MHD equations with zero heat conductivity and initial vacuum in a bounded domain. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Euler-Boussinesq equations in dimension two. Some new regularity criteria via the temperature are established by making use of the Littlewood-Paley technique and the new logarithmic Gronwall inequality. [ABSTRACT FROM AUTHOR]

This paper proves a regularity criterion for the $3D$ full compressible Navier-Stokes-Maxwell system in a bounded domain. [ABSTRACT FROM AUTHOR]

In this paper, we consider the density-dependent Boussinesq equations, and provide a regularity criterion involving the velocity field in BMO space. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new regularity criterion for the 3D incompressible MHD equations involving partial components of the velocity gradient and magnetic fields. [ABSTRACT FROM AUTHOR]

In this paper, we consider the three-dimensional Boussinesq equations, and obtain a logarithmically improved regularity criterion in terms of pressure. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem for the incompressible Navier-Stokes equations in R, and provide a new regularity criterion involving only two entries of the Jacobian matrix of the velocity field. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem for the incompressible Navier-Stokes equations in R, and provide two new regularity criteria involving only two entries of the Jacobian matrix of the velocity field. [ABSTRACT FROM AUTHOR]

We establish some regularity criteria for the incompressible Navier-Stokes equations in a bounded three-dimensional domain concerning the quotients of the pressure, the velocity field and the pressure gradient. [ABSTRACT FROM AUTHOR]

In this paper, we consider the three-dimensional (3D) incompressible Boussinesq equations. We obtain some regularity criteria for the three-dimensional (3D) Boussinesq equations in the Morrey-Campanato space. [ABSTRACT FROM AUTHOR]