11 papers · 1 filter
Quantitative uniqueness for bi-Laplace equations with lower-order coefficients
Zhiwei Wang
We study quantitative unique continuation for bi-Laplace equations \[ Δ^2u+W(x)Δu+V(x)\cdot\nabla u=0 \] with lower-order coefficients. Using the weighted-frequency function,…
Bounds of singular sets for elliptic equations in domains with singular potentials
Zhiwei Wang, Jiuyi Zhu
We study the quantitative codimension-two estimate for the singular set in the boundary neighborhoods of the solutions of \begin{equation*} Δu+V(x)u=0\qquad\text{in }Ω, \qquad u=0\…
Quantitative uniqueness for bi-Laplace equations with potentials
Long Teng, Zhiwei Wang, Jiuyi Zhu
We study quantitative unique continuation for bi-Laplace equations \[Δ^{2}u+V(x)u=0 \] by introducing some new weighted frequency functions. We establish quantitative three-ball in…
Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic space
Zhi-Wei Wang, Samuel L. Braunstein
We prove that the three-dimensional incompressible Navier-Stokes equations with the deformation Laplacian on hyperbolic 3-space $\HH^3$ admit a unique global mild solution for suff…
Exponential stability for the three-dimensional Navier-Stokes equations on negatively curved manifolds
Zhi-Wei Wang, Samuel L. Braunstein
We extend the exponential stability theorem for the three-dimensional incompressible Navier-Stokes equations from hyperbolic 3-space $\HH^3$ (established in a companion paper) to c…
Resolving the viscosity operator ambiguity on Riemannian manifolds via a kinematic selection principle
Zhi-Wei Wang, Samuel L. Braunstein
On a general Riemannian manifold the Navier-Stokes equations admit several inequivalent formulations, differing in the choice of viscous operator: the Hodge Laplacian, the Bochner…
Logarithmic Sobolev inequality and hypercontractivity for the Navier-Stokes Fokker-Planck operator
Zhi-Wei Wang, Samuel L. Braunstein
The stochastic incompressible Navier-Stokes equations on $\TT^3$, completed by the fluctuation-dissipation noise, have a Fokker-Planck generator that decomposes into a self-adjoint…
Exponential thermalisation of viscous fluids on negatively curved manifolds
Samuel L. Braunstein, Zhi-Wei Wang
The deterministic incompressible Navier-Stokes equations are physically incomplete: any viscous fluid at finite temperature must exhibit thermal fluctuations whose form is dictated…
Kinematic selection of the viscous stress in relativistic dissipative hydrodynamics
Zhi-Wei Wang, Samuel L. Braunstein
All standard formulations of relativistic dissipative hydrodynamics, from Eckart through Israel-Stewart to the recent BDNK framework, assume that the viscous stress depends on the…
Boundary conditions select the viscous operator on Riemannian hypersurfaces: formal analysis and rigorous thin-shell limits
Zhi-Wei Wang, Samuel L. Braunstein
A viscous fluid confined to a thin layer around a curved surface is governed, as the layer thickness vanishes, by an effective viscous operator on the surface. We show that the wal…
Quantitative unique continuation for elliptic equations with Hölder continuous potentials
Long Teng, Zhiwei Wang, Jiuyi Zhu
We study quantitative unique continuation for second order elliptic equations with lower-order terms of Hölder regularity via a weighted frequency function method. We establish qua…