Related papers: Solving some Navier-Stokes Equations with the init…
We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on $R^3$. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each…
This paper presents an analytic solution of the incompressible Navier-Stokes equations as recurrence relations for the solution's derivatives, addressing the Clay Mathematics Institute's Millennium Prize problem on Navier-Stokes existence…
We consider global-in-time small mild solutions of the initial value problem to the incompressible Navier-Stokes equations in $R^3$. For such solutions, an asymptotic stability is established under arbitrarily large initial…
We prove the existence of a forward discretely self-similar solutions to the Navier-Stokes equations in $ \Bbb R^{3}\times (0,+\infty)$ for a discretely self-similar initial velocity belonging to $ L^2_{ loc}(\Bbb R^{3})$.
In this paper, we obtain explicit solutions to the Navier-Stokes equation and the Euler equation. For any initial velocity u0 and the force vector f, exact solutions can be explicitly solved as series, where the coefficients are all known…
We consider 3d Navier-Stokes system with periodic boundary conditions for small initial data from the space of Pseudomeasures. We provide asymptotic behavior for the coefficients in the perturbation series for the solution of this system.
In this paper we prove that the Navier-Stokes initial value problem (1) has a unique smooth local strong solution and if the following condition are satisfied (1) and is H\"older continuous about on, (2) The initial value
We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus $g(\mathcal{S})$. The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding…
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…
The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous…
We present a novel approach to the Liouville problem for the stationary Navier-Stokes equations. As an application of our method, we prove conditional Liouville theorems with assumptions on the antiderivative of the velocity that represent…
In this article we study some problems related to the incompressible 3D Navier-Stokes equations from the point of view of Lebesgue spaces of variable exponent. These functional spaces present some particularities that make them quite…
The Navier-Stokes-Fourier system is a well established model for describing the motion of viscous compressible heat-conducting fluids. We study the existence of time-periodic weak solutions and improve the known result in the following…
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…
We prove some estimates for suitable weak solutions to the non-stationary three-dimensional Navier-Stokes equations under assumptions that certain invariant functionals of the velocity are bounded.
We prove, with a more geometric approach, that the solutions to the Navier-Stokes equations are regular up to a set of Hausdorff dimension 1. The main tool for the proof is a new compactness lemma and the monotonicity property of harmonic…
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 study Liouville-type results for the stationary Navier--Stokes equations in $\mathbb{R}^3$. We prove that any $\dot{H}^1(\mathbb{R}^3)$ solution is trivial under an integrability condition imposed only on the radial component of the…
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…
In this article, we establish sufficient conditions for the regularity of solutions of Navier-Stokes equations based on one of the nine entries of the gradient tensor. We improve the recently results of C.S. Cao, E.S. Titi (Arch. Rational…