Problem For Equations Of Motion Research Articles

Spatial flow around an obstacle of a mixture of compressible viscous fluids

We present results on the existence and uniqueness of a strong solution to the inhomogeneous boundary value problem for equations of motion of viscous compressible fluids mixture with three spatial variables.

Mixed initial–boundary value problem for equations of motion of Kelvin–Voigt fluids

The initial–boundary value problem for equations of motion of Kelvin–Voigt fluids with mixed boundary conditions is studied. The no-slip condition is used on some portion of the boundary, while the impermeability condition and the tangential component of the surface force field are specified on the rest of the boundary. The global-in-time existence of a weak solution is proved. It is shown that the solution is unique and depends continuously on the field of external forces, the field of surface forces, and initial data.

Solvability for equations of motion of weak aqueous polymer solutions with objective derivative

In this paper we consider the initial-boundary problem for equations of motion of weak aqueous polymer solutions involving the regularized Jaumann’s derivative. We prove the weak solvability of the model in space E1={v:v∈L∞(0,T;V1),v′∈L2(0,T;V−1)} using the topological approximation approach.

On the uniqueness problem for the metric of the first approximation in general-relativistic mechanics

It is shown that it is worthwhile to connect the correctness problem for the relativistic equations of motion with the problem of a correct metric of the first approximation. Many questions and problems in the description of motion, which have been considered on the basis of the relativistic equations of motion, turn out to be solvable using the first-approximation metric only.

Attractors of initial boundary value problems for equations of motion of Jeffreys-Oldroyd fluids in domains with nonsmooth and smooth boundaries

Attractor theory of the initial boundary value problems with adhesion and slippage boundary conditions for equation of motion of Jeffreys-Oldroyd fluids in domains with smooth and nonsmooth boundary is developed. Bibliography: 34 titles.

The solvability of the initial boundary-value problem for equations of motion of a viscous compressible barotropic liquid in the spacesW 2 l+1,l/2+1 (Q T )

A new method of estimating the solutions of the Navier-Stokes equations for a viscous compressible barotropic fluid in a bounded domain {Omega} {contained_in} R{sup 3} suggested, which makes it possible to investigate the problem for the whole scale of anisotropic spaces W{sub 2}{sup l+2, l/2+1} (Q{sub T}), Q{sub T} = {Omega} x (0,T), for arbitrary l > 1/2.

Certain nonlocal problems for two-dimensional equations of motion of Oldroyd fluids

The solvability of a boundary-value problem on the semi-axis t≥0 is studied for two-dimensional equations of motion of Oldroyd fluids (1), and with “trivial problem data” a proof is given of the existence of a solution which is periodic with respect to t and has the period ω. This solution has an absolute term which is also periodic with respect to t and has the period ω. Substantiation is given for the principle of linearization (first Liapunov method) in the theory of the exponential stability of solutions at t→∞.

Dynamical system generated by the equations of motion of an Oldroyd fluid of order L

The attractor m and dynamical system {m;Vt,−∞<t<∞} of the initial-boundary problem for the two-dimensional equations of motion of an Oldroyd fluid of order L are constructed.

Attractors and dynamical systems generated by initial-boundary problems for the equations of motion of viscoelastic fluids

Attractors m and dynamical systems {m; Vt,−∞<t<∞} generated by initial-boundary problems for the two-dimensional equations of motion of Oldroyd fluids of order L=1,2,... and the three-dimensional equations of motion of Kelvin-Voight fluids of order L=0,1,2,... are described.

Initial-boundary-value problems for equations of motion of nonlinear viscoelastic fluids

One proves an existence theorem “in the large” for a generalized solution in the sense of O. A. Ladyzhenskaya of the initial-boundary-value problem for the equation of motion of nonlinear viscoelastic fluids, whose special cases are the weakly con-centrated aqueous solutions of polymers.