Related papers: Quantitative lower bound for lifespan for solution…
We prove that the multidimensional dimensional initial value problem for the Navier-Stokes equations is globally well-posed in the so-called Moment and Grand Lebesgue Spaces (GLS), and give some a priory estimations for solution in this…
The purpose of this article is to establish bounds from below for the life span of regular solutions to the incompressible Navier-Stokes system, whichinvolve norms not only of the initial data, but also of nonlinear functions of the initial…
In this paper, we study the initial and boundary value problem of the Navier-Stokes equations in the half space. We prove the unique existence of weak solution $u\in L^q(\R_+\times (0,T))$ with $\nabla u\in L^{\frac{q}{2}}_{loc}(\R_+\times…
We study the initial-boundary value problem of the stochastic Navier--Stokes equations in the half space. We prove the existence of weak solutions in the standard Besov space valued random processes when the initial data belong to the…
We offer a simple Monte-Carlo method for solving of the multidimensional initial value and non-homogeneous problem for the Navier-Stokes Equations in whole space when the initial function and right hand side belong to the correspondent…
The aim of the note is to discuss different definitions of solutions to the Cauchy problem for the Navier-Stokes equations with the initial data belonging to the Lebesgue space $L_3(\mathbb R^3)$
This paper addresses a question concerning the behaviour of a sequence of global solutions to the Navier-Stokes equations, with the corresponding sequence of smooth initial data being bounded in the (non-energy class) weak Lebesgue space…
In this work, we are interested in the link between strong solutions of the Boltzmann and the Navier-Stokes equations. To justify this connection, our main idea is to use information on the limit system (for instance the fact that the…
We provide a new lower bound for the life span of solutions to the Kirchhoff equation for which the initial data belongs to the Gevrey space. This lower bound strictly improves the classical one in the case when the frequency spectrum of…
In the paper, we have introduced the notion of mild bounded ancient solutions to the Navier-Stokes equations in a half space. They play a certain role in understanding whether or not solutions to the initial boundary value problem for the…
We consider mild solutions to the Navier-Stokes initial-value problem which belong to certain ranges…
This paper discusses the solvability (global in time) of the initial-boundary value problem of the Navier-stokes equations in the half space when the initial data $ h\in \dot{ B}_{q \sigma}^{\alpha-\frac{2}{q}}(\R_+)$ and the boundary data…
In this paper, we study the initial-boundary value problem of the Navier-Stokes system in the half space. We prove the unique solvability of the weak solution on some short time interval (0, T) with the velocity in $C^{\alpha, \frac12…
We consider the Navier-Stokes equations in $\mathbb{R}^3$ subject to the initial condition with initial velocity field in $L^{2}_{\rm loc} (\mathbb{R}^3)$ such that $\limsup_{R \to +\infty } R^{-1} \|u_{0} \|_{ L^{2}(B(R))} < +\infty$. Our…
In this paper, we study the initial value problem of the Navier-Stokes equations in the half-space. Let a solenoidal initial velocity be given in the function space $ \dot{B}_{pq,0}^{\alpha-\frac{2}{2}}({\mathbb R}^n_+)$ for $\alpha +1 =…
In this paper, we consider the initial value problem for nonlinear wave equation with weighted nonlinear terms in one space dimension. Kubo & Osaka & Yazici(2013) studied global solvability of the problem under different conditions on the…
In this paper, we investigate the link between kinetic equations (including Boltzmann with or without cutoff assumption and Landau equations) and the incompressible Navier-Stokes equation. We work with strong solutions and we treat all the…
In this paper, we establish the global existence of small solutions to the inhomogeneous Navier-Stokes system in the half-space. The initial density only has to be bounded and close enough to a positive constant, and the initial velocity…
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.
An initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations is investigated. After transforming the system into Lagrangian coordinate, the resulting system possesses a structure with uniform…