Global dissipative solutions of the defocusing isothermal Euler–Langevin–Korteweg equations

We construct global dissipative solutions on the torus of dimension at most three defocusing isothermal Euler–Langevin–Korteweg system, which corresponds to Euler–Korteweg system compressible quantum fluids with an pressure law and a linear drag term respect velocity. In particular, feature prevents energy BD-entropy from being positive. Adapting standard approximation arguments we first show existence weak Navier–Stokes–Langevin–Korteweg system. Introducing relative entropy function satisfying Gronwall-type inequality then perform inviscid limit obtain