After reviewing the source-type solution of Burgers equation with standard dissipativity, we study hypoviscous counterpart equation. 1) We determine an that governs near-identity transformation underlying its self-similar solution. 2) develop approximation scheme and construct first-order approximation. 3) obtain numerically by Newton-Raphson iteration find it to agree well Implications are giv...

Landau solutions are special to the stationary incompressible Navier-Stokes equations in three dimensional space excluding origin. They self-similar and axisymmetric with no swirl. In fact, any smooth solution must be a solution. effort of extending this result one for class pointwise scale-invariant bound $|u(x)|\leq C_0|x|^{-1}$ some $C_0>0$, we consider discretely solutions, investigate exis...

The main goal of this paper is to analyze a family "simplest possible" initial data for which, as shown by numerical simulations, the incompressible Euler equations have multiple solutions. We take here first step toward rigorous validation these results. Namely, we consider system corresponding self-similar solution, restricted bounded domain with smooth boundary. ...

We formalise a systematic method of constructing forward self-similar solutions to the Navier-Stokes equations in order characterise late stage decaying process turbulent flows. (i) In view critical scale-invariance type 2 we exploit vorticity curl as dependent variable derive and analyse dynamically-scaled equations. This formalism offers viewpoint from which problem takes simplest possible fo...