Drifting Solutions with Elliptic Symmetry for the Compressible Navier-Stokes Equations with Density-dependent Viscosity

Abstract

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen in [Yuen M.W. (2008), Analytical Solutions to the Navier-Stokes Equations, J. Math. Phys. 49, 113102], our solutions constitute a generalization of that obtained by Yuen.

9 pages. Key Words: Compressible Navier-Stokes Equations, Characteristic Method, Elliptic Symmetry, Generalized Emden System, Drifting Solutions

References in corpus (3)

• Analytical Solutions to the Navier-Stokes Equations
• Self-Similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^{N}
• Perturbational Blowup Solutions to the 1-dimensional Compressible Euler Equations