iscous two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations. In this paper the solvability of the related stationary problems is discussed and computational results are presented. Furthermore, it is shown that depending on the flow parameters like viscosity or density ratios and on the fluxes there can happen nonexistence of steady‐state solutions. For other parameter sets the solution is even unique.
Apie dviejų tekančių kanale skysčių srauto egzistavimą ir vienatį
Santrauka. Dviejų, tekančių kanale, klampių skysčių srauto uždavinys iškyla taikant įvairias skirtingų rūšių paviršių padengimo technologijas. Atitinkamas matematinis modelis išreiškiamas dvimačių kraštinių uždavinių su laisvu paviršiumi Navje‐Stokso lygtims. Straipsnyje nagrinėjamas santykinai stacionaraus uždavinio išsprendžiamumas ir pateikiami skaičiavimo rezultatai. Be to parodoma, kad priklausomai nuo srovės parametrų kaip ir nuo klampumo ir tankio santykio stacionarūs sprendiniai gali neegzistuoti. Su kitais parametrais egzistuoja tiksliai vienas sprendinys.
Socolowsky, J. (2004). On the existence and uniqueness of two‐fluid channel flows. Mathematical Modelling and Analysis, 9(1), 67-78. https://doi.org/10.3846/13926292.2004.9637242
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