Related papers: Dissipation and Regularity in the Smagorinsky Mode…
We consider a finite element method which couples the continuous Galerkin method away from internal and boundary layers with a discontinuous Galerkin method in the vicinity of layers. We prove that this consistent method is stable in the…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
In this paper, we establish the pseudospectral bound for the linearized operator of the Navier-Stokes equations around the 3D Kolmogorov flow. Using the pseudospectral bound and the wave operator method introduced in [LWZ], we prove the…
We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
We consider a family of Leray-$\alpha$ models with periodic boundary conditions in three space dimensions. Such models are a regularization, with respect to a parameter $\theta$, of the Navier-Stokes equations. In particular, they share…
We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an…
General scenario of turbulence theory is proposed and applied to streaky wall-bounded turbulence. This scenario introduces a new field of transverse waves. Significance of the theory rests on a mathematical theorem associated with the…
This article presents a comprehensive analysis of the formation and dissipation of vortices within chaotic fluid flows, leveraging the framework of Sobolev and Besov spaces on Riemannian manifolds. Building upon the Navier-Stokes equations,…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
We prove the existence and uniqueness of strong solutions to the steady isentropic compressible Navier-Stokes equations with inflow boundary conditions for density and mixed boundary conditions for the velocity around a shear flow. In…
Kelvin's Theorem on conservation of circulations is an essential ingredient of G. I. Taylor's theory of turbulent energy dissipation by the process of vortex-line stretching. In previous work, we have proposed a nonlinear mechanism for the…
We develop a sharp maximal regularity theory for the resolvent and evolution Stokes equations with no-slip boundary conditions, focusing on bounded domains of low regularity. Our framework covers the full scales of Besov and Sobolev spaces,…
This paper investigates the stochastic tamed 3D Navier-Stokes equations with locally weak monotonicity coefficients in the whole space as well as in the three-dimensional torus, which play a crucial role in turbulent flows analysis. A…
Anomalous dissipation, the persistence of a finite mean kinetic energy dissipation as the Reynolds number tends to infinity, occurs in flows with sufficiently spatially rough velocity fields. Compressible turbulence adds further anomalous…
The no-slip boundary condition results in a velocity shear forming in fluid flow near a solid surface. This shear flow supports the turbulence characteristic of fluid flow near boundaries at Reynolds numbers above $\approx1000$ by making…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
A novel route to instabilities and turbulence in fluid and plasma flows is presented in kinetic Vlasov-Maxwell model. New kind of flow instabilities is shown to arise due to the availability of new kinetic energy sources which are absent in…
Singularity of Navier-Stokes equations is uncovered for the first time which explains the mechanism of transition of a smooth laminar flow to turbulence. It is found that when an inflection point is formed on the velocity profile in…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…