This note looks at the two similarity solutions of the Navier-Stokes equations in polar coordinates. In the second solution an initial value problem is reduced into generalized stationary KDV and hence integrable.
A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conse...A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.展开更多
The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is a...The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is applied perpendicular to the plate and the fluid motion is subjected to a uniform suction and injection. Similarity transformations are employed to reduce the non-linear equations governing the flow under discussion to two ordinary differential equations （with and without dispersion terms）. Using the finite difference scheme, numerical solutions represented by graphs with reference to the various involved parameters of interest are discussed and appropriate conclusions are drawn.展开更多
文摘This note looks at the two similarity solutions of the Navier-Stokes equations in polar coordinates. In the second solution an initial value problem is reduced into generalized stationary KDV and hence integrable.
文摘A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.
文摘The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is applied perpendicular to the plate and the fluid motion is subjected to a uniform suction and injection. Similarity transformations are employed to reduce the non-linear equations governing the flow under discussion to two ordinary differential equations （with and without dispersion terms）. Using the finite difference scheme, numerical solutions represented by graphs with reference to the various involved parameters of interest are discussed and appropriate conclusions are drawn.
