Fujita-Kato Theorem for the Inhomogeneous Incompressible Navier-Stokes Equations with Nonnegative Density
Year: 2023
Author: Jianzhong Zhang, Hongmei Cao
Communications in Mathematical Research , Vol. 39 (2023), Iss. 1 : pp. 79–106
Abstract
In this paper, we prove the global existence and uniqueness of solutions for the inhomogeneous Navier-Stokes equations with the initial data $(\rho_0,u_0)\in L^∞\times H^s_0$, $s>\frac{1}{2}$ and $||u_0||_{H^s_0}\leq \varepsilon_0$ in bounded domain $\Omega \subset \mathbb{R}^3$, in which the density is assumed to be nonnegative. The regularity of initial data is weaker than the previous $(\rho_0,u_0)\in (W^{1,\gamma}∩L^∞)\times H^1_0$ in [13] and $(\rho_0,u_0)\in L^∞\times H^1_0$ in [7], which constitutes a positive answer to the question raised by Danchin and Mucha in [7]. The methods used in this paper are mainly the classical time weighted energy estimate and Lagrangian approach, and the continuity argument and shift of integrability method are applied to complete our proof.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0034
Communications in Mathematical Research , Vol. 39 (2023), Iss. 1 : pp. 79–106
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Inhomogeneous Navier-Stokes equations nonnegative density global existence and uniqueness.