## On the steady transport equation.(English)Zbl 0941.35079

Málek, J. (ed.) et al., Advanced topics in theoretical fluid mechanics. Lectures of the 5th Winter School on mathematical theory in fluid mechanics, Paseky nad Jizerou, Czech Republic, December 6-14, 1997. Harlow: Longman. Pitman Res. Notes Math. Ser. 392, 118-146 (1998).
This lecture note deals in details with the transport equation $$\lambda x+w. \nabla x+gx=f$$, $$\lambda\in\mathbb{R}$$, $$w,g$$ and $$f$$ are given functions on a given domain $$\Omega$$. The main issues herein considered are the following ones. After a careful description of the function spaces in which the problem is considered, one states existence theorems for strong solutions and for weak solutions and studies the asymptotic properties of $$L^q$$-solutions. Finally, some results are stated on the transport equation in the divergence form.
For the entire collection see [Zbl 0927.00030].

### MSC:

 35Q35 PDEs in connection with fluid mechanics 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35D05 Existence of generalized solutions of PDE (MSC2000) 35B40 Asymptotic behavior of solutions to PDEs