Self Similar Solutions P.-Y. Lagr´ee CNRS & UPMC Univ Paris 06, UMR 7190, Institut Jean Le Rond ∂’Alembert, Boˆıte 162, F-75005 Paris, France pyl@ccr.jussieu.fr ; .lmm.jussieu.fr/∼lagree Looking at self similar solution is a common tool in fluid mechanics. It seem...
It is shown how to find all its quasi-homogeneous (self-similar) solutions by the support of the equation with the help of Linear Algebra computations. The simplifications of such an equation are studied with the help of power and logarithmic transformations. It is shown that these ...
We construct self-similar solutions for three-dimensional incom- pressible Navier-Stokes equations, providing some examples of func- tional spaces where this can be done. We apply our results to a par- ticular case of L 2 initial data. Introduction We are interested in the Navier-Stokes equa...
self-similar solutions/ A4755C Jets in fluid dynamics A4725 Turbulent flows, convection, and heat transferSimilarity solutions for incompressible axisymmetric jets using a k - and a constant eddy diffusivity turbulence models are considered. For the k - model, the governing equations are very ...
Self-Similar Solutions of the Second KindIn recent years there has been a surge of interest in self-similar solutions of the second kind. Such solutions are not newly discovered; they had been identified and in fact so named by Zel'dovich inL. A. Peletier...
We study cavitating solutions to compressible Navier–Stokes equations with degenerate density-dependent viscosity. We consider two types of small radial solutions: forward self-similar (expanders), and backward self-similar (shrinkers). In the first case, we construct such solutions by a fixed-...
Damped wave equation Self-similar variables Asymptotic behavior Self-similar solutions a b s t r a c t We consider the damped hyperbolic equation εuττ+ uτ= (a(ξ)uξ)ξ− |u|p−1u, (ξ,τ) ∈ R × R+, (1) where ε > 0,a(ξ) → 1 as |ξ| → +∞ and 1 ...
, , The Navier-Stokes equation with distributions as initial data and appli- cation to self-similar solutions. New trends in microlocal analysis (Tokyo, 1995), 125-141, Springer, Tokyo, 1997.H. Kozono and M. Yamazaki: The Navier-Stokes equation with dis- tributions as initial data and ...
self-similar solutions for the “dam break” and the base-level lowering are presented. While the linear case corresponds to the classic diffusion equation, the main effect of the nonlinearity appears to be the presence of singularities in the self-similar solutions, related to the finite speed ...
Self-similar solutions of a fast diffusion equation that do not conserve mass Mark A. Peletier Technische Universiteit Delft Delft, The Netherlands Hongfei Zhang Ball State University Muncie, Indiana, USA Abstract We consider self-similar solutions of the fast diffusion equation u...