The mathematical model of compressible fluid flow

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. Spūdau skysčio tekėjimo matematinis modelis Santrauka 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.  First Published Online: 14 Oct 201

Existence and asymptotic behaviour of steady flow of a viscous barotropic gas in a pipe

Existence and asymptotic behaviour of steady flow of a viscous barotropic gas in a pipe is analyzed

Time periodic Navier–Stokes equations in a thin tube structure

International audienceThe time periodic Navier-Stokes equations are considered in the three-dimensional and two-dimensional settings with Dirichlet boundary conditions in thin tube structures. These structures are finite union of thin cylinders (thin rectangles in the case of dimension two), where the small parameter ε is the ratio of the hight and the diameter of the cylinders. We consider the case of finite or big coefficient before the time derivative. This setting is motivated by hemodynamical applications. Theorems of existence and uniqueness of a solution are proved. Complete asymptotic expansion of a solution is constructed and justified by estimates of the difference of the exact solution and truncated series of the expansion in norms taking into account the first and second derivatives with respect to the space variables and the first derivative in time. The method of asymptotic partial decomposition of the domain is justified for the time periodic problem