arXiv subjects

Jingwen Han

Publications and source records attributed to Jingwen Han.

5 recordsLinked to original sources

arXiv2026

uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab

In this paper, we investigate the uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab domain with no-slip boundary conditions. Specifically, under the given external force and the small Poiseuille flow assumptions, we prove that there is an H1 solution, and obtain the pointwise decay around the Poiseuille flow at far field. Furthermore, if the force is small, the solution is shown to be unique. The key point of the proof is the estimate of the Dirichlet integral of the solutions in the truncated domains and the Stokes regularity estimates.

math.AP↗

arXiv2026

Liouville-type theorems for the stationary non-Newtonian fluids in a slab

In this paper, we investigate Liouville-type theorems for stationary solutions to the shear thickening fluid equations in a slab. We show that the axisymmetric solution must be trivial if its local $L^\infty$-norm grows mildly as the radius $R$ grows. Also, a bounded general solution $u$ must be trivial if $ru^r$ is bounded. The proof is inspired by the work of Bang, Gui, Wang, and Xie [J. Fluid Mech. 1005 (2025)] for the Navier-Stokes equations, and the key point is to establish a Saint-Venant type estimate that characterizes the growth of the local Dirichlet integral of nontrivial solutions. One new ingredient is the estimate of the constant in Korn's inequality over different domains.

math.AP↗

arXiv2024

Liouville-type theorems for Axisymmetric solutions to steady Navier-Stokes system in a layer domain

In this paper, we investigate the Liouville-type theorems for axisymmetric solutions to steady Navier-Stokes system in a layer domain. The both cases for the flows supplemented with no-slip boundary and Navier boundary conditions are studied. If the width of the outlet grows at a rate less than $R^{\frac{1}{2}}$, any bounded solution is proved to be trivial. Meanwhile, if the width of the outlet grows at a rate less than $R^{\frac{4}{5}}$, every D-solution is proved to be trivial. The key idea of the proof is to establish a Saint-Venant type estimate that characterizes the growth of Dirichlet integral of nontrivial solutions.

math.AP↗

arXiv2024

Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$

We show that any bounded smooth helically symmetric solution $(\Bu, \Bh)$ in $\mathbb{R}^3$ must be constant vectors. This is an extension of previous result \cite[Theorem 1.1]{HWXAHE} from Navier-Stokes system to MHD system. The proof relies on establishing a Saint-Venant type estimate to characterize the growth of Dirichlet integral of nontrivial solutions.

math.AP↗

arXiv2023

Liouville-type theorems for steady Navier-Stokes system under helical symmetry or Navier boundary conditions

In this paper, the Liouville-type theorems for the steady Navier-Stokes system are investigated. First, we prove that any bounded smooth helically symmetric solution in $\mathbb{R}^3$ must be a constant vector. Second, for steady Navier-Stokes system in a slab supplemented with Navier boundary conditions, we prove that any bounded smooth solution must be zero if either the swirl or radial velocity is axisymmetric, or $ru^{r}$ decays to zero as $r$ tends to infinity. Finally, when the velocity is not big in $L^{\infty}$-space, the general three-dimensional steady Navier-Stokes flow in a slab with the Navier boundary conditions must be a Poiseuille type flow. The key idea of the proof is to establish Saint-Venant type estimates that characterize the growth of Dirichlet integral of nontrivial solutions.

math.AP↗