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

Abstract EN

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.