We discuss the kinetic formulation of nonlinear
conservation laws and related equations,
a kinetic formulation which describes both the equation and
the entropy criterion. This formulation is a kinetic one,
involving an additional variable called
velocity by analogy. We apply this
formulation to derive, based upon the velocity averaging
lemmas, new compactness and regularity results.
In particular, we highlight the regularizing effect
of nonlinear entropy solution operators, and we quantify the gained
regularity in terms of the nonlinearity.
Finally, we show that this kinetic formulation is
in fact valid and meaningful for more general classes of
equations, including equations involving
nonlinear second-order terms,
and the 
hyperbolic
system of isentropic gas dynamics, in both Eulerian or
Lagrangian variables ( - the so called 'p-system').
)
)
isentropic equations