Related papers: Multi-dimensional Jordan chain and Navier-Stokes E…
We investigate a coupling between the compressible Navier-Stokes-Fourier system and the full Maxwell-Stefan equations. This model describes the motion of chemically reacting heat-conducting gaseous mixture. The viscosity coefficients are…
We introduce new classes of solutions to the three dimensional Navier-Stokes equations in the whole and half spaces that add rotational correction to self-similar and discretely self-similar solutions. We construct forward solutions in…
A proof is given of the global existence and uniqueness of a weak solution to Navier-Stokes boundary problem. The proof is short and essentially self-contained.
We study the limit of the stochastic model for two dimensional second grade fluids subjected to the periodic boundary conditions as the stress modulus tends to zero. We show that under suitable conditions on the data the whole sequence of…
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 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…
We consider special solution to the 3D compressible Navier-Stokes system with and without the Coriolis force and dry friction and find the respective initial data implying a finite time gradient catastrophe.
Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing…
We study the two-dimensional Navier-Stokes system on a flat cylinder with the usual Dirichlet boundary conditions for the velocity field u. We formulate the problem as an infinite system of ODE's for the natural Fourier components of the…
We study the variety of complex $n$-dimensional Jordan algebras using techniques from Geometric Invariant Theory.
We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least $n$. In the operator case, it was recently…
A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution…
In this note we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data.
Two novel frameworks for handling mathematical and physical problems are introduced. The first, the emerging Jordan form, generalizes the concept of the Jordan canonical form, a well-established tool of linear algebra. The second, dual…
Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a…
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…
The square peg problem asks whether every Jordan curve in the plane has four points which form a square. The problem has been resolved (positively) for various classes of curves, but remains open in full generality. We present two new…
We prove the existence of solutions for the axisymmetric steady Navier-Stokes system around an infinite cylinder under external forces. The solutions are constructed to be decaying at the horizontal infinity, despite an analogue of the…
It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for the…
In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted…