Related papers: Some interesting class of integrable partial diffe…
The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations --…
A Navier--Stokes system on a curve is discussed. The quotient equation for this system is found. The quotient is used to find some solutions of Navier--Stokes system. Using virial expansion of the Planck potential, we reduce the quotient…
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
We obtain the global large solutions to the compressible Navier-Stokes equations in $\mathbb{R}^2$. The solution is large in the sense that there is no smallness assumption applied to one component of the initial incompressible velocity.
The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including…
Weak solutions of incompressible Navier-Stokes Equations re-obtained variationally
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
We study a system of nonlinear partial differential equations describing the unsteady motions of incompressible chemically reacting non-Newtonian fluids. The system under consideration consists of the generalized Navier-Stokes equations…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
The existence and uniqueness of global regular solution of incompressible Navier-Stokes equations in $\mathbb{R}^3$ are derived provided the initial velocity vector field holds a special structure.
For a class of evolution equations that possibly have only local solutions, we introduce a stochastic component that ensures that the solutions of the corresponding stochastically perturbed equations are global. The class of partial…
In this paper, we study the regularity problem of the 3D incompressible Navier\~nStokes equations. We prove that the strong solution exists globally for new regularity criteria. For negligible forces, we give an improvement of the known…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…
A family of solutions of the Jacobi PDEs is investigated. This family is $n$-dimensional, of arbitrary nonlinearity and can be globally analyzed (thus improving the usual local scope of Darboux theorem). As an outcome of this analysis it is…
This paper provides mathematical analysis of an elementary fully discrete finite difference method applied to inhomogeneous (non-constant density and viscosity) incompressible Navier-Stokes system on a bounded domain. The proposed method…
We have developed dynamic manifold solutions for the Navier-Stokes equations using an extension of differential geometry called the calculus for moving surfaces. Specifically, we have shown that the geometric solutions to the Navier-Stokes…
The micropolar equations are a useful generalization of the classical Navier-Stokes model for fluids with micro-structure. We prove the existence of global and strong solutions to these equations in cylindrical domains in $\mathbb{R}^3$. We…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…