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 approximation system 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>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference30 articles.
1. H. Abidi, G. L. Gui, P. Zhang, On the wellposedness of three-dimensional inhomogeneous Navier-Stokes equations in the critical spaces, Arch. Ration. Mech. Anal., 204 (2012), 189–230. https://doi.org/10.1007/s00205-011-0473-4
2. H. Abidi, P. Zhang, Global well-posedness of 3-D density-dependent Navier-Stokes system with variable viscosity, Sci. China Math., 58 (2015), 1129–1150. https://doi.org/10.1007/s11425-015-4983-7
3. H. Abidi, P. Zhang, On the global well-posedness of 2-D inhomogeneous incompressible Navier-Stokes system with variable viscous coefficient, J. Differ. Equ., 259 (2015), 3755–3802. https://doi.org/10.1016/j.jde.2015.05.002
4. R. A. Adams, J. J. F. Fournier, Sobolev spaces, 2 Eds., Elsevier, 2003.
5. S. A. Antontesv, A. V. Kazhikov, Mathematical study of flows of nonhomogeneous fluids, Lecture Notes, Novosibirsk, USSR: Novosibirsk State University, 1973.