On the stationary transport equations. (English) Zbl 1139.35327
Summary: We find solutions in \(L^{1}\) and \(L^\infty \) for the general domains for certain transport equations arising in the theory of the compressible Navier-Stokes equations. Some a priori estimates in \(L^{1}\) and \(L^\infty \) have been found. Then, the asymptotic behavior of \(L^\infty \) solutions is found. We also consider solutions in \(\mathcal H^1\) and BMO. We show the uniqueness of the solutions in these four function spaces.
MSC:
35D05 | Existence of generalized solutions of PDE (MSC2000) |
35B65 | Smoothness and regularity of solutions to PDEs |
35L60 | First-order nonlinear hyperbolic equations |
35Q30 | Navier-Stokes equations |
35B45 | A priori estimates in context of PDEs |
35D10 | Regularity of generalized solutions of PDE (MSC2000) |
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