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Abstract
In this note we consider the mathematical model of the isothermal compressible fluid flow in an exterior domain O ⊂ R3. In order to solve this problem we apply a decomposition scheme and reduce the nonlinear problem to an operator equation with a contraction operator. After the decomposition the nonlinear problem splits into three linear problems: Neumann‐like problem, modified Stokes problem and transport equation. These linear problems are solved in weighted function spaces with detached asymptotics.
Šiame darbe išnagrinetas spūdaus skysčio tekejimo išorineje srityje O ⊂ R3 matematinis modelis. Šios problemos sprendimui pritaikyta dekompozicijos schema, kuri leidžia netiesini uždavini suskaidyti i tris paprastesnius tiesinius uždavinius: Neimano tipo, modifikuota Stokso ir transporto. Šiu tiesiniu uždaviniu sprendiniu ieškota specialiose svorinese funkciju erdvese su atskirta asimptotika. Suformuluotos teoremos apie minetu tiesiniu ir netiesinio uždaviniu sprendinio egzistencija ir vienati. Pateikti irodymu pagrindiniai žingsniai.
Notes
This work was supported by Lithuanian State Science and Foundation grant A‐524.