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The equation of potential flows of a compressible viscous fluid at small Reynolds numbers: Existence, uniqueness, and stabilization of solutions. (English. Russian original) Zbl 0806.76077
Sib. Math. J. 34, No. 3, 457-467 (1993); translation from Sib. Mat. Zh. 34, No. 3, 70-80 (1993).
We consider the boundary value problem for the model system of equations \(\mu\Delta \vec u+(\lambda+ \mu)\nabla (\text{div } \vec u)- \nabla p=0\), \({{\partial\rho} \over {\partial t}}+ \text{div}(\rho\vec u)=0\), \(p=p(\rho)\). From a mechanical standpoint, such an approximation to the Navier-Stokes equations is justified when the Reynolds number is small, i.e. in the case of highly viscous fluids. Our aim is to prove solvability for the problem in various functional classes, establish uniqueness for a solution under certain assumptions on smoothness, and prove stabilization for a solution at infinite time.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
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