相关论文: Determining modes for the 3D Navier-Stokes equatio…
We study blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the 3D Euler equations, where the sense of convergence and self-similarity are considered in various sense. We extend much further, in…
In this work, we consider time-fractional Navier-Stokes equations (NSE) with the external forces involving finite delay. Equations are considered on a bounded domain in 3-D space having sufficiently smooth boundary. We transform the system…
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 both deterministic and stochastic 2D Navier Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev…
Navier-Stokes equations in the whole space R^3 subject to an anisotropic viscosity and a random perturbation of multiplicative type is described. By adding a term of Brinkman-Forchheimer type to the model, existence and uniqueness of global…
We present exact solutions of the incompressible Navier-Stokes equations in a background linear shear flow. The method of construction is based on Kelvin's investigations into linearized disturbances in an unbounded Couette flow. We obtain…
A blowup criteria along maximum point of the 3D-Navier-Stokes flow in terms of function spaces with variable growth condition is constructed. This criterion is different from the Beale-Kato-Majda type and Constantin-Fefferman type…
In this paper, we first obtain the temporal decay estimates for weak solutions to the three dimensional generalized Navier-Stokes equations. Then, with these estimates at disposal, we obtain the temporal decay estimates for higher order…
We consider the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. We prove the local existence and uniqueness of the strong solution in a…
We are concerned with the global existence of classical solutions to the barotropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. We demonstrate that the classical solutions…
The limit resonant equation of the 3D rotating Navier-Stokes equations is obtained by taking large rotation limit. This equation has a nonlinear term with restricted interactions between Fourier modes, and thus it enjoys better regularity…
The purpose of this paper is to study the vanishing viscosity limit for the d-dimensional Navier--Stokes equations in the whole space: \begin{equation*} \begin{cases} \partial_tu^\varepsilon+u^\varepsilon\cdot \nabla…
We consider some complex-valued solutions of the Navier-Stokes equations in $R^{3}$ for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of…
We consider the stochastic damped Navier-Stokes equations in $\mathbb R^d$ ($d=2,3$), assuming as in our previous work [4] that the covariance of the noise is not too regular, so It\^o calculus cannot be applied in the space of finite…
In this paper, we study the quantitative regularity and blowup criteria for classical solutions to the three-dimensional incompressible Navier-Stokes equations in a critical Besov space framework. Specifically, we consider solutions $u\in…
Limit behaviors of blow up solutions for impressible Navier-Stokes equations are obtained.
In this article, a perturbation theory of the compressible Navier-Stokes equations in $\mathbb{R}^n$ $(n \geq 3)$ is studied to investigate decay estimate of solutions around a non-constant state. As a concrete problem, stability is…
We present different classes of initial data to the three-dimensional, incompressible Navier-Stokes equations, which generate a global in time, unique solution though they may be arbitrarily large in the end-point function space in which a…
This paper establishes bounds on norms of all orders for solutions on the global attractor of the 2D Navier-Stokes equations, complexified in time. Specifically, for periodic boundary conditions on $[0,L]^2$, and a force…
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…