49 research outputs found
From the highly compressible Navier-Stokes equations to the Porous Medium equation - rate of convergence
We consider the one-dimensional Cauchy problem for the Navier-Stokes
equations with degenerate viscosity coefficient in highly compressible regime.
It corresponds to the compressible Navier-Stokes system with large Mach number
equal to for going to . When
the initial velocity is related to the gradient of the initial density, a
solution to the continuity equation- converges to the unique
solution to the porous medium equation [13,14]. For viscosity coefficient
with , we obtain a
rate of convergence of in ; for the solution
converges in . For compactly
supported initial data, we prove that most of the mass corresponding to
solution is located in the support of the solution to the
porous medium equation. The mass outside this support is small in terms of
.Comment: 19 page
Incompressible limit of the Navier-Stokes model with a growth term
Starting from isentropic compressible Navier-Stokes equations with growth
term in the continuity equation, we rigorously justify that performing an
incompressible limit one arrives to the two-phase free boundary fluid system
On strong dynamics of compressible two-component mixture flow
We investigate a system describing the flow of a compressible two-component
mixture. The system is composed of the compressible Navier-Stokes equations
coupled with non-symmetric reaction-diffusion equations describing the
evolution of fractional masses. We show the local existence and, under certain
smallness assumptions, also the global existence of unique strong solutions in
framework. Our approach is based on so called entropic variables
which enable to rewrite the system in a symmetric form. Then, applying
Lagrangian coordinates, we show the local existence of solutions applying the
- maximal regularity estimate. Next, applying exponential decay
estimate we show that the solution exists globally in time provided the initial
data is sufficiently close to some constants. The nonlinear estimates impose
restrictions . However, for the purpose of generality
we show the linear estimates for wider range of and