相关论文: On Bridging Analyticity and Sparseness in Hyperdis…
The goal of this note is to demonstrate that as soon as the hyper-diffusion exponent is greater than one, a class of finite time blow-up scenarios consistent with the analytic structure of the flow (prior to the possible blow-up time) can…
We study the three-dimensional incompressible Navier-Stokes system on $\mathbb{R}^3$ with an additional dissipative nonlocal term \[ \partial_t u + (u\cdot\nabla)u + \nabla p = \nu \Delta u + Lu, \qquad {\rm div}\, u = 0, \] where $L$ is a…
It is shown that, if the vorticity magnitude associated with a (presumed singular) three-dimensional incompressible Navier-Stokes flow blows-up in a manner exhibiting certain {\em time dependent local structure}, then {\em time independent}…
We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak…
We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…
This paper concerns the 3-dimensional Lagrangian Navier-Stokes $\alpha$ model and the limiting Navier-Stokes system on smooth bounded domains with a class of vorticity-slip boundary conditions and the Navier-slip boundary conditions. It…
We investigate the inertial limit of the compressible Navier--Stokes system posed on the $3$-dimensional torus, and allowing for regions of vacuum. Considering global-in-time finite-energy weak solutions of a scaled system, we rigorously…
We approximate a two--phase model by the compressible Navier-Stokes equations with a singular pressure term. Up to a subsequence, these solutions are shown to converge to a global weak solution of the compressible system with the congestion…
In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical measure associated with the particle system converges…
We consider a statistical limit of solutions to the compressible Navier--Stokes system in the high Reynolds number regime in a domain exterior to a rigid body. We investigate to what extent this highly turbulent regime can be modeled by an…
We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
This paper extends the weak solution theory for the 3D Navier-Stokes equations of Barker, Seregin and Sverak from a critical setting to a supercritical setting making sure to include a useful a priori energy bound as well as a statement…
Resolvent analysis provides a framework to predict coherent spatio-temporal structures of largest linear energy amplification, through a singular value decomposition (SVD) of the resolvent operator, obtained by linearizing the Navier-Stokes…
We introduce an algorithm for estimating the entropy of pairwise, probabilistic graph models by leveraging bridges between social communities and an accurate entropy estimator on sparse samples. We propose using a measure of investment from…
We construct solutions to the randomly-forced Navier--Stokes--Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense…
We study the 4-dimensional pressureless Navier--Stokes-Poisson equations with density-dependent viscosity. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper.
We consider enstrophy dissipation in two-dimensional (2D) Navier-Stokes flows and focus on how this quantity behaves in thelimit of vanishing viscosity. After recalling a number of a priori estimates providing lower and upper bounds on this…
This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…
A numerical method for the two-dimensional, incompressible Navier--Stokes equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving…