coupled systems of Stokes type
turbulent flow
weak solution
Poisson equation in L^1
On the existence of weak solutions to a coupled system
Joachim Naumann
Naumann
Joachim
Jörg Wolf
Wolf
Jörg
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976), 12, 39
Joachim Naumann
,
Jörg Wolf
Preprint series:
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976), 12, 39
MSC 2000
 35J55 Boundary value problems for elliptic systems

35Q30 Stokes and NavierStokes equations

76F25 Turbulent transport, mixing
Abstract
In this paper, we study a model problem for the
stationary turbulent motion of two fluids in disjoint bounded
domains $\Omega_1$ and $\Omega_2$ such that $\Gamma:=\bar{\Omega}_1 \cap \bar{\Omega}_2 \not= \varnothing$. The specific difficulty of this problem arises from the boundary condition which characterizes the interaction of the fluid motions along $\Gamma$.\par
We prove the existence of a weak solution to the problem under consideration which is more regular than the solution obtained in [3]. Moreover, we establish some regularity results for any weak solution. Our discussion is heavily based on the results in appendices 1 and 2 which seem to be of independent interest.
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