Related papers: Existence and uniqueness for plane stationary Navi…
Here we investigate the Cauchy problem for the barotropic Navier-Stokes equations in R^n, in the critical Besov spaces setting. We improve recent results as regards the uniqueness condition: initial velocities in critical Besov spaces with…
Different authors had received a lot of results regarding the Euler and Navier-Stokes equations. Existence and smoothness of solution for the Navier-Stokes equations in two dimensions have been known for a long time. Leray showed that the…
Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier-Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the…
We consider the two-dimensional Navier-Stokes system in a domain exterior to a disk. The system admits a stationary solution with critical decay $O(|x|^{-1})$ written as a linear combination of the pure rotating flow and the flux carrier.…
The stationary Navier--Stokes--Cahn--Hilliard equations are considered, governing the motion of a compressible, two-phase fluid mixture with a diffuse interface. The free energy density in this paper has a singular logarithmic…
In this paper, the Liouville-type theorems for the steady Navier-Stokes system are investigated. First, we prove that any bounded smooth helically symmetric solution in $\mathbb{R}^3$ must be a constant vector. Second, for steady…
We consider the stationary incompressible Navier Stokes equation in the exterior of a disk B with non-zero Dirichlet boundary conditions on the disk and zero boundary conditions at infinity. We prove the existence of solutions for an open…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
Due to computational complexity, fluid flow problems are mostly defined on a bounded domain. Hence, capturing fluid outflow calls for imposing an appropriate condition on the boundary where the said outflow is prescribed. Usually, the…
We prove existence of global regular axially-symmetric solutions to the Navier-Stokes equations in a cylindrical domain. We assume the periodic boundary conditions on the top and the bottom of the cylinder, but on the lateral part we assume…
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 show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles…
This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton…
We prove the existence and uniqueness of solutions to the time-dependent incompressible Navier-Stokes equations with a free-boundary governed by surface tension. The solution is found using a topological fixed-point theorem for a nonlinear…
Using ODE-methods and trapping regions derived by Mattingly and Sinai we give a new proof of the existence and uniqueness of solutions to Navier-Stokes equations with periodic boundary conditions on the plane.
We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional…
We study the Navier-Stokes system describing the motion of a compressible viscous fluid driven by a nonlinear multiplicative stochastic force. We establish local in time existence (up to a positive stopping time) of a unique solution, which…
For the $3D$ fractional Navier--Stokes equations perturbed by transport noise, we prove the existence of infinitely many H\"older continuous analytically weak, probabilistically strong Leray--Hopf solutions starting from the same…
The weak solution to the Navier-Stokes equations in a bounded domain $D \subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all $t \geq 0$. In a…
In this article the question on uniqueness of weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case is studied. Here the investigation is carried out with use of another approach. The uniqueness of velocity…