A note on viscous conservation laws with complex characteristics
There are several physical set-ups involving multi-phase fluids that result in highly unstable behavior already at rather low flow rates. Mathematical models of these flow problems consist typically of conservation laws like conservation of mass and momentum for each phase together with coupling terms connecting the phases. For multi-phase flow the characteristics are often complex and without the dissipative terms the problem is ill-posed and not computable. We will discuss why the nonlinearity of the system can prevent blow-up.
complex characteristics the principle of frozen coefficients