A New Pressure Regularity Criterion of the Three-Dimensional Micropolar Fluid Equations

This paper concerns the regularity criterion of the weak solutions to the three-dimensional (3D) micropolar fluid equations in terms of the pressure. It is proved that if one of the partial derivatives of pressure satisfies ∂3π∈Lp(0,T;Lq(R3)) with 2/p+3/q≤2,3<q<∞,1<p<∞, then the weak solution of the micropolar fluid equations becomes regular on (0,T]

Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t)-3/4≤uL2≤C2(1+t)-3/4,  t>1. The decay rate is optimal since it coincides with that of heat equation

A New Pressure Regularity Criterion of the Three-Dimensional Micropolar Fluid Equations

This paper concerns the regularity criterion of the weak solutions to the three-dimensional (3D) micropolar fluid equations in terms of the pressure. It is proved that if one of the partial derivatives of pressure satisfies 3 ∈ (0, ; (R 3 )) with 2/ + 3/ ≤ 2, 3 &lt; &lt; ∞, 1 &lt; &lt; ∞, then the weak solution of the micropolar fluid equations becomes regular on (0, ]