The shock-change equations

I have now published a summary of the shock change-equations and their use for evolution equations of shocks.  The relations relate the shock speed, acceleration and curvature to the flow derivatives behind the shock, controlling the shock motion.

Physics of Fluids 32, 056106 (2020); https://doi.org/10.1063/1.5140216

For example, the relation between the shock speed, acceleration and curvature with the rate of expansion of the gas behind the shock, essential in modelling of reactive gas dynamics along a particle path, is

$$\frac{1}{\rho }\frac{\text{D}\rho }{\text{D}t}=\frac{2\left(\left(3M_w^2+1\right){\dot{M}}_w\left(\gamma +1\right)+c_0\kappa \left(M_w^2-1\right)\left(2+M_w^2\left(\gamma -1\right)\right)\right)}{M_w\left(M_w^2-1\right){\left(\gamma +1\right)}^2}.$$ or for a strong shock: $$\frac{\left(\gamma -1\right)S_w}{{\rho }_0{\dot{S}}_w}\frac{\text{D}\rho }{\text{D}t}=6+\frac{2\left(\gamma -1\right)}{\left(\gamma +1\right)}\frac{S_w^2\kappa }{{\dot{S}}_w}$$