On the stationary transport equations

We find solutions in L1L1 and L∞L∞ for the general domains for certain transport equations arising in the theory of the compressible Navier–Stokes equations. Some a priori estimates in L1L1 and L∞L∞ have been found. Then, the asymptotic behavior of L∞L∞ solutions is found. We also consider solutions in H1H1 and BMO. We show the uniqueness of the solutions in these four function spaces.