Traveling Wave Solutions to Brenner-Navier-Stokes-Fourier system

As a continuum model for compressible fluid flows, Howard Brenner proposed the so-called Brenner-Navier-Stokes-Fourier(BNSF) system that improves some flaws of the Navier-Stokes-Fourier(NSF) system. For BNSF system, the volume velocity concept is introduced and is far different from the mass velocity of NSF, since the density of a compressible fluid is inhomogeneous. Although BNSF was introduced more than ten years ago, the mathematical study on BNSF is still in its infancy. We consider the BNSF system in the Lagrangian mass coordinates. We prove the existence and uniqueness of monotone traveling wave solutions to the BNSF system. We also present some quantitative estimates for them.