Related papers: Existence Theorems for Regular Spatially Periodic …
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…
A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…
The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in $H^1$ initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of…
In this paper, we study existence times of strong solutions of the three-dimensional Navier-Stokes equations in time-varying analytic Gevrey classes based on Sobolev spaces $H^s, s> \frac{1}{2}$. This complements the seminal work of Foias…
We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of data allowing growth at spatial infinity. Namely, we show the global existence of suitable weak solutions when the initial data…
We consider the modified Navier-Stokes equations in R3 describing the motion of a fluid in the presence of a rotating rigid body. Weighted Sobolev spaces are used to describe the behavior of solutions at large distances. Under suitable…
We establish global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In this setting, solutions are expected to have space regularity…
Regularity properties of strong solutions are considered.
We study the theory of local and global strong solution for the stochastic tamed Navier--Stokes equations with multiplicative Wiener and L\'evy jump noise in the whole space $\R^3$. More specifically, we first prove the existence of a…
We show existence and uniqueness for small data of regular time-periodic solutions to the Navier-Stokes problem in the exterior of a rigid body, $\mathscr B$, that moves by time-periodic translational motion of the same period along a…
In this paper we establish the local-in-time existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in three-dimensional space. The vanishing density and temperature…
In this paper we consider the r\^ole that numerical computations -- in particular Galerkin approximations -- can play in problems modelled by the 3d Navier-Stokes equations, for which no rigorous proof of the existence of unique solutions…
We show global existence and non-uniqueness of probabilistically strong, analytically weak solutions of the three-dimensional Navier-Stokes equations perturbed by Stratonovich transport noise. We can prescribe either: \emph{i}) any…
We construct a solution to the spatially periodic $d$-dimensional Navier-Stokes equations with a given distribution of the initial data. The solution takes values in the Sobolev space $H^\alpha$, where the index $\alpha\in R$ is fixed…
For the 3D Navier-Stokes-Maxwell problem on the whole space and in the presence of external time-periodic forces, first we study the existence of time-periodic small solutions, and then we prove their asymptotic stability. We use new type…
This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant coefficients.…
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…
In this paper, we use forward-backward stochastic differential systems to study the solution of two and d dimensional ($d\geq 3$) Navier-Stokes-$\alpha$ equation. For the two dimensional Navier-Stokes-$\alpha$ equation with space periodic…
We address the local well-posedness for the stochastic Navier-Stokes system with multiplicative cylindrical noise in the whole space. More specifically, we prove that there exists a unique local strong solution to the system in…
The Navier-Stokes equation on Rd (d greater or equal to 3) formulated on Besov spaces is considered. Using a stochastic forward-backward differential system, the local existence of a unique solution in B_ r, with r > 1 + d is obtained. We…