  After reviewing the source-type solution of the Burgers equation with
standard dissipativity, we study the hypoviscous counterpart of the Burgers
equation. 1) We determine an equation that governs the near-identity
transformation underlying its self-similar solution. 2) We develop its
approximation scheme and construct the first-order approximation. 3) We obtain
the source-type solution numerically by the Newton-Raphson iteration scheme and
find it to agree well with the first-order approximation. Implications of the
source-type solution are given, regarding the possibility of linearisation of
the hypoviscous Burgers equation. Finally we address the problems of the
incompressible fluid equations in two dimensions, centering on the surface
quasi-geostrophic equation with standard and hypoviscous dissipativity.
