Piotr Gwiazda, Polish Academy of Sciences
We consider a combined system of Euler, Euler–Korteweg and Euler–Poisson equations with friction and exponential pressure with exponent \(\gamma>1\). We show the existence of dissipative measure-valued solutions in the cases of repulsive and attractive potential in Euler–Poisson system. The latter case requires additional restriction on \(\gamma\). Furthermore in case of \(\gamma\ge 2\) we show that the strong solutions to the Cahn–Hillard–Keller–Segel system are a high-friction limit of the dissipative measure-valued solutions to Euler–Korteweg–Poisson equations.