Global Kato’s Solutions for Inhomogeneous Navier–Stokes System in \({L^{3}(\mathbb{R}^{3})}\)
Abstract
Abstract. We consider the global-in-time well-posedness of Cauchy problem for the inhomogeneous Navier–Stokes system in critical spaces [Formula: see text] with small data in the sense of Kato’s solution [ 14 ]. When the initial velocity [Formula: see text] is small in the critical space [Formula: see text], and when the initial density [Formula: see text] with small fluctuation is away from vacuum, the global-in-time solutions in [Formula: see text] to the inhomogeneous Navier–Stokes system have been constructed with the help of the [Formula: see text]regularity argument, a refined estimate of pressure and a covering argument.
Fields of Study & Subjects
Navier-Stokes equation solutions
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 2
- Pages
- 730–774
- Publication date
- 26 February 2026
- Language
- EN