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.
Spūdaus skysčio tekėjimo matematinis modelis
Santrauka. Šiame darbe išnagrinėtas spūdaus skysčio tekėjimo išorinėje srityje O ⊂ R3 matematinis modelis. Šios problemos sprendimui pritaikyta dekompozicijos schema, kuri leidžia netiesinį uždavinį suskaidyti į tris paprastesnius tiesinius uždavinius: Neimano tipo, modifikuotą Stokso ir transporto. Šių tiesinių uždavinių sprendinių ieškota specialiose svorinėse funkcijų erdvėse su atskirta asimptotika. Suformuluotos teoremos apie minėtų tiesinių ir netiesinio uždavinių sprendinio egzistencija ir vienatį. Pateikti įrodymu pagrindiniai žingsniai.
Leonavičiene, T., & Pileckas, K. (2002). The mathematical model of compressible fluid flow. Mathematical Modelling and Analysis, 7(1), 117-126. https://doi.org/10.3846/13926292.2002.9637184
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