On the stability of solutions to the 3-D anisotropic Navier-Stokes equations in the critical space
Year: 2026
Type: preprint
Abstract: In this paper, we study the continuous dependence of solutions to the three-dimensional incompressible anisotropic Navier-Stokes equations $(ANS)$ with initial data in the critical space $\dot{B}^{0,\frac12}$. We prove that the data-to-solution map is continuous in this setting. Due to the critical regularity of the problem, the classical Bona-Smith argument \cite{BoSm} (see also the abstract result \cite{ABITZ}) does not appear to apply because a key ingredient (the Lipschitz continuity at lower regularity) does not appear to hold. As a consequence, we develop a new direct Fourier-weighted method within the Besov framework.
Source: arXiv (Cornell University)
Authors: Burq, Nicolas, Liu, Ning, Zhang, Ping
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3683686157, G6291648921, G8533620077
OpenAlex ID: W7213312128