Sentence examples for a viscous problem from inspiring English sources

In Section 3, we present a viscous problem of Eq. (1) and give a corresponding well-posedness result.

It is well known that the small viscous problem is a challenge subject due to the singularity of the numerical solutions.

In Section 3, we present the viscous problem and give a corresponding well-posedness result.

Afterward, the published research articles with regard to solving a viscous fluid problem in a tube in cylindrical coordinates have emerged continuously.

Finally the IFR method is applied to simulate viscous flow pass a cylinder at Reynolds number 150 to show its capability for viscous problem.

Namely, the strong convergence of q ε is necessary to be established if we want to send ε to zero in the viscous problem (11).

The existence of a weak solution to the Cauchy problem (4) will be established by proving compactness of a sequence of smooth functions { u ε } ε > 0 solving the following viscous problem: { ∂ u ε ∂ t + u ε ∂ u ε ∂ x − γ α 2 ∂ u ε ∂ x + ∂ P ε ∂ x = ε u x x, P ε = Λ − 2 [ 1 2 u ε 2 − γ α 2 u ε − α 2 2 ( ∂ u ε ∂ x ) 2 − f ( u ε ) ], u ε ( 0, x ) = u ε, 0. (11).

To establish the existence of solutions to Cauchy problem (5), we will analyze the limiting behavior of a sequence of smooth functions { u ε } ε > 0, where each function u ε satisfies the viscous problem { ∂ t u ε − ∂ t x x 3 u ε + m u ε ∂ x u ε = 3 ∂ x u ε ∂ x x 2 u ε + u ε ∂ x x x 3 u ε + ε ∂ x x 2 u ε − ε ∂ x x x x 4 u ε, ( t, x ) ∈ R + × R, u ε ( 0, x ) = u 0, ε ( x ), x ∈ R, (7).

Our approach here ignores inertial effects; thus the motion is only correct as an approximation for very viscous problems.

In this paper, we present a stable hybrid scheme for viscous problems.

This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems.