Steady-state buoyancy-driven viscous flow with measure data. (English) Zbl 0981.35054

Roubíček, Tomáš

Math. Bohem. 126, No. 2, 493-504 (2001).

Summary: A steady-state system of equations for incompressible, possibly non-Newtonean fluids of the \(p\)-power is studied. Viscous flow coupled with the heat equation is considered in a smooth bounded domain \(\Omega \subset {\mathbb R}^n\), \(n=2\) or 3, with heat sources allowed to have a natural \(L^1\)-structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if \(p>3/2\) (for \(n=2\)) or if \(p>9/5\) (for \(n=3\)).

MSC:

35Q35	PDEs in connection with fluid mechanics
76A05	Non-Newtonian fluids
35J60	Nonlinear elliptic equations
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

non-Newtonean fluids; heat equation; dissipative heat; adiabatic heat; viscous flow; existence of a distributional solution; small data