On 3D slightly compressible Euler equations.
On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat concluding capillary fluid. The inequality is essential in proving the global existence of solutions.
On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat conducting fluid. The inequality is essential in proving the global existence of solutions.
On a free boundary barotropic model
On a low Mach nuclear core model
We propose to formally derive a low Mach number model adapted to the modeling of a water nuclear core (e.g. of PWR- or BWR-type) in the forced convection regime or in the natural convection regime by filtering out the acoustic waves in the compressible Navier-Stokes system. Then, we propose a monodimensional stationary analytical solution with regular and singular charge loss when the equation of state is a stiffened gas equation. Moreover, we show...
On an estimate for the linearized compressible Navier-Stokes equations in the -framework
An -estimate with a constant independent of time for solutions of the linearized compressible Navier-Stokes system in the whole space (under the assumption that solutions have compact supports in space) is obtained.
On an inequality for a free boundary problem for equations of a viscous compressible heat-conducting capillary fluid
We derive an inequality for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. This inequality is crucial to proving the global existence of solutions belonging to certain anisotropic Sobolev-Slobodetskiĭ spaces and close to an equilibrium state.
On bounded solutions of one-dimensional compressible Navier-Stokes equations
On dynamics of fluids in meteorology
We consider the full Navier-Stokes-Fourier system of equations on an unbounded domain with prescribed nonvanishing boundary conditions for the density and temperature at infinity. The topic of this article continues author’s previous works on existence of the Navier-Stokes-Fourier system on nonsmooth domains. The procedure deeply relies on the techniques developed by Feireisl and others in the series of works on compressible, viscous and heat conducting fluids.
On global motion of a compressible barotropic viscous fluid with boundary slip condition
Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ with the boundary slip condition is proved. The solution is close to an equilibrium solution. The proof is based on the energy method. Moreover, in the -approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to and the density belongs to , α ∈ (1/2,1).
On local motion of a compressible barotropic viscous fluid bounded by a free surface
We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the existence time....
On local motion of a general compressible viscous heat conducting fluid bounded by a free surface
The motion of a viscous compressible heat conducting fluid in a domain in ℝ³ bounded by a free surface is considered. We prove local existence and uniqueness of solutions in Sobolev-Slobodetskiĭ spaces in two cases: with surface tension and without it.
On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids
The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the -framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the -approach, because the velocity belongs to with r > 3.
On measure solutions to the zero-pressure gas model and their uniqueness
On measure solutions to the Zero-pressure gas model and their uniqueness
The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized...
On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface [Book]
On nonstationary motion of a fixed mass of a general fluid bounded by a free surface
In the paper the motion of a fixed mass of a viscous compressible heat conducting fluid is considered. Assuming that the initial data are sufficiently close to an equilibrium state and the external force, the heat sources and the heat flow through the boundary vanish, we prove the existence of a global in time solution which is close to the equilibrium state for any moment of time.
On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary
The motion of a fixed mass of a viscous compressible heat conducting capillary fluid is examined. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global-in-time solution which is close to the constant state for any moment of time. Moreover, we present an analogous result for the case of a barotropic viscous compressible fluid.
On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary
On nonviscous compressible fluids in a time-dependent domain