arXiv subjects
Publications and source records attributed to Youseung Cho.
We establish a new Liouville-type theorem for the stationary Navier--Stokes equations in $\mathbb{R}^3$. The main result is an improvement of the previous result with a logarithmic factor based on an understanding of $L^p$ growth of the velocity field near infinity.
We establish various results concerning the uniqueness of zero velocity solutions for the static barotropic Navier--Stokes system. Some of them can be seen as Liouville-type theorems for problems in unbounded physical space.
We study the Liouville-type theorem for smooth solutions to the steady 3D tropical climate model. We prove the Liouville-type theorem if a smooth solution satisfies a certain growth condition in terms of $L^p$-norm on annuli, which improves the previous results, Theorem 1.1 (Math. Methods Appl. Sci. 44, 2021) by Ding and Wu, and Theorem 1.1 and Theorem 1.2 (Appl. Math. Lett. 138, 2023) by Yuan and Wang.
In this paper, we study the Liouville-type property for smooth solutions to the steady 3D tropical climate model. We prove that if a smooth solution $(u,v,θ)$ satisfies $u \in L^3 (\mathbb{R}^3)$, $v \in L^2 (\mathbb{R}^3)$, and $\nabla θ\in L^2 (\mathbb{R}^3)$, then $u=v=0$ and $θ$ is constant, which improves the previous result, Theorem 1.3 (Math. Methods Appl. Sci. 44, 2021) by Ding and Wu.