Related papers: Forward self-similar solutions to the 2D Navier--S…
The Navier-Stokes-Voigt equations are a regularization of the Navier-Stokes equations that share some of its asymptotic and statistical properties and have been used in direct numerical simulations of the latter. In this article we…
The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary…
It is well known that the solution of the 3d Navier--Stokes equations remains bounded if the initial data and the forcing are sufficiently small relative to the viscosity, and for a finite time given any bounded initial data. In this…
We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…
Based on Makino's solutions with radially symmetry, we extend the corresponding ones with elliptic symmetry for the compressible Euler and Navier-Stokes equations in R^{N} (N\geq2). By the separation method, we reduce the Euler and…
The Navier-Stokes equations describing laminar flow of an incompressible fluid will be solved. Different group of general solutions for Navier stokes equations governing Laminar incompressible fluids will be derived.
We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions $n\leq 4$.…
The aim of this paper is to solve the three dimensional Navier-Stokes problem with conservative source term. We use convolution methods to construct "well behaved" smooth solutions of the initial boundary value problem for the system of…
A coupled forward-backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier-Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the…
We study the removable singularity problem for $(-1)$-homogeneous solutions of the three-dimensional incompressible stationary Navier-Stokes equations with singular rays. We prove that any local $(-1)$-homogeneous solution $u$ near a…
The present paper deals with existence and uniqueness of global mild solutions for the 2D Navier-Stokes equations with impulses. Using the framework of nonautonomous dynamical systems, we extend previous results considering the 2D…
In this paper, we consider the model of 3D incompressible Navier-Stokes equations and 2D supercritical Surface Quasi-Geostrophic equations with time oscillation in the nonlinear term. We obtain that there exists global smooth solution of…
We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of…
We study the so-called damped Navier-Stokes equations in the whole 2D space. The global well-posedness, dissipativity and further regularity of weak solutions of this problem in the uniformly-local spaces are verified based on the further…
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated…
Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data.…
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 analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in…
The three-dimensional, homogeneous, incompressible Navier-Stokes equations are studied in the absence of viscosity in one direction. It is shown that there are arbitrarily large initial data generating a unique global solution, the main…
We consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the…