If $B_{y1}=B_{y2}=0$, alignment also gives $u_{y1}=u_{y2}=0$. The common normal magnetic field contributes the same constant magnetic stress on both sides and carries no Poynting flux in the aligned frame. The remaining mass, normal-momentum, and energy conditions are therefore exactly
$$
[\rho u_x]=0,
\qquad
[\rho u_x^2+p]=0,
\qquad
\left[\frac12u_x^2+h\right]=0,
$$
which are the <Rankine-Hugoniot conditions for a perfect gas>.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 314 / 3 / d / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-314/3/d/i/solution