On the Leray problem and the Poiseuille flow. (English) Zbl 1493.35064
Let \(\Omega\) denote a smooth open domain in \(\mathbb R^n\). The author considers the classic boundary value problem for the stationary nonhomogeneous Navier-Stokes equations in a weak statement. Existence and uniqueness are studied by application of the Lax-Milgram and the Schauder fixed point theorems. Uniqueness is proved for sufficiently large viscosity. The special attention is paid to the Poiseuille flow when \(\Omega = \mathbb R \times \omega\), where \(\omega\) is a bounded domain in \(\mathbb R^{n-1}\).
Reviewer: Vladimir Mityushev (Kraków)
MSC:
| 35Q30 | Navier-Stokes equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35J60 | Nonlinear elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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