相关论文: Self-similar source-type solutions to the three-di…

We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existence of small shrinkers.

The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…

We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…

The goal of this paper is to provide an algorithm that, for any sufficiently localised, divergence-free small initial data, explicitly constructs a localised external force leading to a rapidly dissipative solutions of the Navier-Stokes…

We positively answer Question 2.2 and Question 2.3 in [Bru\`e, De Lellis, 2023] in dimension $4$ by building new examples of solutions to the forced $4d$ incompressible Navier-Stokes equations, which exhibit anomalous dissipation, related…

We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from…

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations…

We study a nonlinear coupled fluid-structure system modelling the blood flow through arteries. The fluid is described by the incompressible Navier-Stokes equations in a 2D rectangular domain where the upper part depends on a structure…

In this paper, a lower bound estimate on the uniform radius of spatial analyticity is established for solutions to the incompressible, forced Navier-Stokes system on an n-torus. This estimate improves or matches previously known estimates…

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…

The aim of this work is to prove an existence and uniqueness result of Kato-Fujita type for the Navier-Stokes equations, in vorticity form, in $2-D$ and $3-D$, perturbed by a gradient type multiplicative Gaussian noise (for sufficiently…

We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…

This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…

We consider the 2D incompressible Navier-Stokes equations on $\mathbb{T}\times \mathbf{R}$, with initial vorticity that is $\delta$ close in $H^{log}_xL^2_{y}$ to $-1$(the vorticity of the Couette flow $(y,0)$). We prove that if $\delta\ll…

This paper is concerned with quantitative estimates for the Navier-Stokes equations. First we investigate the relation of quantitative bounds to the behaviour of critical norms near a potential singularity with Type I bound…

The velocity-vorticity formulation of the 3D Navier-Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose a new regularization of the 3D Navier-Stokes equations,…

In 2004, Dombrowski et al. showed that suspensions of aerobic bacteria often develop flows from the interplay of chemotaxis and buoyancy, which is described as the chemotaxis-Navier-Stokes model, and they observed self-concentration occurs…

We study the two-dimensional Navier-Stokes system on a flat cylinder with the usual Dirichlet boundary conditions for the velocity field u. We formulate the problem as an infinite system of ODE's for the natural Fourier components of the…

A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…

The aim of this note is to present the recent results in [Buckmaster, Cao-Labora, G\'omez-Serrano, arXiv:2208.09445, 2022], concerning the existence of "imploding singularities" for the 3D isentropic compressible Euler and Navier-Stokes…