Existence of global solution to 3D density-dependent incompressible Navier-Stokes equations

Abstract

<abstract><p>In this article, we are committed to studying the three-dimensional incompressible Navier-Stokes equations, where the viscosity depends on density according to a power law. We investigate the Cauchy problem by constructing an approximated solution and bootstrap argument. Finally, we establish the existence of a global strong solution under the conditions of small initial data and the compatibility condition. Meanwhile, the algebraic decay-in-time rates for the solution are also obtained. It is worth pointing out that the degradation of viscosity is allowed.</p></abstract>