Related papers: Sharp non-uniqueness of solutions to stochastic Na…
In this paper, we study the global regularity of strong solution to the Cauchy problem of 3D incompressible Navier-Stokes equations with large data and non-zero force. We prove that the strong solution exists globally for $\nabla u\in…
The initial problem for the Navier-Stokes type equations over ${\mathbb R}^n \times [0,T]$, $n\geq 2$, with a positive time $T$ in the spatially periodic setting is considered. First, we prove that the problem induces an open injective…
We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier--Stokes equation driven by a spatially real-analytic multiplicative and transport noise but emanating from an initial condition that is only…
In this paper we study the uniqueness property of solutions to the steady incompressible Euler equations with perturbations in $\Bbb R^N$. Our perturbations include as special cases the Euler equations with a `single signed' nonlinear term,…
High-order time-stepping schemes are crucial for simulating incompressible fluid flows due to their ability to capture complex turbulent behavior and unsteady motion. In this work, we propose a third-order accurate numerical scheme for the…
In this paper, we give a sufficient condition to guarantee the existence of a smooth solution of the Navier-Stokes Equation with the nice decreasing properties at infinity. In this way, we prove the existence of smooth physically reasonable…
We show that weak solutions of degenerate Navier-Stokes equations converge to the strong solutions of the pressureless Euler system with linear drag term, Newtonian repulsion and quadratic confinement. The proof is based on the relative…
This paper deals with time-fractional stochastic Navier-Stokes equations, which are characterized by the coexistence of stochastic noise and a fractional power of the Laplacian. We establish sufficient conditions for the existence and…
We consider the strong solution of the 2D Navier-Stokes equations in a torus subject to an additive noise. We implement a fully implicit time numerical scheme and a finite element method in space. We prove that the rate of convergence of…
This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach,…
We consider parabolic variational inequalities in a Hilbert space $V$, which have a non-monotone nonlinearity of Navier--Stokes type represented by a bilinear operator $B: V \times V \to V'$ and a monotone type nonlinearity described by a…
We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike the solutions constructed in \cite{albritton2021non}, the solutions we construct live at a supercritical scaling, in…
The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations of incompressible fluid turbulence with…
We study the 2D Navier-Stokes equations within the framework of a constraint that ensures energy conservation throughout the solution. By employing the Galerkin approximation method, we demonstrate the existence and uniqueness of a global…
In this paper, we consider the smooth solutions of 3D incompressible Navier-Stokes equations in periodic domains. We prove that, in the absence of external forces and with divergence-free smooth periodic initial data, periodic smooth…
Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some numerical evidences that the Navier-Stokes equations admit…
The aim of the note is to proof a regularity result for weak solutions to the Navier-Stokes equations that are locally in $L_\infty(L^{3,\infty})$. It reads that, in a sense, the number of singular points at each time is at most finite. Our…
This paper examines the uniqueness/non-uniqueness of local-in-time strong solutions for the incompressible 3D Navier-Stokes equations in bounded domains, which are $\partial_t u=\nu \Delta u- u\cdot \nabla u-\nabla p+ f$ and $div~u=0$. The…
In this paper, we investigate the initial-boundary value problem to the heat conductive compressible Navier-Stokes equations. Local existence and uniqueness of strong solutions is established with any such initial data that the initial…
We show that any Leray-Hopf weak solution to the $d$-dimensional Navier-Stokes equations $(d\geq 3)$ with initial values $u_0\in H^{s}(\mathbb R^d)$, $s\geq -1+\frac{d}{2}$, belongs to $L^\infty(0,\infty; H^{s}(\mathbb R^d))$ and thus it is…