相关论文: Pseudospectrum for Oseen vortices operators
Navier-Stokes equations are investigated in a functional setting in 3D open sets, bounded or not, without assuming any regularity of the boundary. The main idea is to find a correct definition of the Stokes operator in a suitable Hilbert…
We consider the incompressible Navier-Stokes equations in a bounded domain with $\mathcal{C}^{1,1}$ boundary, completed with slip boundary condition. Apart from studying the general semigroup theory related to the Stokes operator with…
We consider the axisymmetric Navier-Stokes equations in a finite cylinder $\Omega\subset\mathbb{R}^3$. We assume that $v_r$, $v_\varphi$, $\omega_\varphi$ vanish on the lateral part of boundary $\partial\Omega$ of the cylinder, and that…
Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model…
In this paper, we investigate the quasi-neutral limit of Nernst-Planck-Navier-Stokes system in a smooth bounded domain $\Omega$ of $\mathbb{R}^d$ for $d=2,3,$ with ``electroneutral boundary conditions" and well-prepared data. We first prove…
Using the example of such a complicated problem as the Cauchy problem for the Navier-Stokes equation, we show how the Poincar\'e-Riemann-Hilbert boundary value problem enables us to construct effective estimates of solutions for this case.…
Linearisation of the Navier-Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier-Stokes equations can be…
We developed analytic approach to the non-planar loop equation, which we derived in previous papers \cite{M19a},\cite{M19b},\cite{M19c}. We found quadratic integral equation for the vorticity distribution $\Omega(r)$ we introduced on a…
We extend our earlier \beta-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687--701] to a rotating sphere. Specifically, we show that the solution of the Navier--Stokes equations on a sphere rotating with angular velocity…
We show that $L_{3,\infty}$-solutions to the three-dimensional Navier-Stokes equations near a flat part of the boundary are smooth.
Based on Leray's formulation of the Navier-Stokes equations and the conditions of the exact linear representation of the nonlinear problem found in this paper, a compact explicit expression for the exact operator solution of the…
We consider the stationary (time-independent) Navier-Stokes equations in the whole threedimensional space, under the action of a source term and with the fractional Laplacian operator (--$\Delta$) $\alpha$/2 in the diffusion term. In the…
We consider the Navier-Stokes equations in the layer ${\mathbb R}^n \times [0,T]$ over $\mathbb{R}^n$ with finite $T > 0$. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes…
We prove Li--Yau-type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier--Stokes equations.
Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier-Stokes equations, which involve the fractional Laplacian operator…
We study controllability issues for the Navier-Stokes Equation on a two dimensional rectangle with so-called Lions boundary conditions. Rewriting the Equation using a basis of harmonic functions we arrive to an infinite-dimensional system…
The Navier-Stokes-$\alpha$ equations belong to the family of LES (Large Eddy Simulation) models whose fundamental idea is to capture the influence of the small scales on the large ones without computing all the whole range present in the…
We show that the solutions to the non-stationary Navier-Stokes equations in $R^d$, $d=2,3$ which are left invariant under the action of discrete subgroups of the orthogonal group $O(d)$ decay much faster as $|x|\to\infty$ or $ t \to\infty$…
We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting…
In this article, we investigate the stabilizability of the two- and three-dimensional Navier-Stokes equations with memory effects around a non-constant steady state using a localized interior control. The system is first linearized around a…