## Journals

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### Open Access Journals

CPAA

An initial-boundary value problem of the three-dimensional incompressible magnetohydrodynamic (MHD) equations is considered in a bounded domain. The homogeneous Dirichlet boundary
condition is prescribed on the velocity, and the perfectly conducting
wall condition is prescribed on the magnetic field. The existence and
uniqueness is established for both the local strong solution with large initial data and the global strong solution with small initial
data. Furthermore, the weak-strong uniqueness of solutions is also proved, which shows that the weak solution is equal to the strong solution with certain initial data.

PROC

A mathematical model for viscous compressible realistic reactive flows
without species diffusion in dynamic combustion is investigated. The initial-boundary
value problem with Dirichlet-Neumann mixed boundaries in a finite domain is studied.
The existence, uniqueness, and regularity of global solutions are established
with general large initial data in $H^1$. It is proved that, although the solutions have
large oscillations and the chemical reaction generates heat, there is no shock wave,
turbulence, vacuum, mass or heat concentration developed in a finite time.

keywords:
real flow
,
reacting fluid
,
Combustion
,
existence
,
a-priori estimates.
,
uniqueness
,
global solutions

CPAA

The equations for viscous, compressible, heat-conductive, real
reactive flows in dynamic combustion are considered, where the
equations of state are nonlinear in temperature unlike the linear
dependence for perfect gases. The initial-boundary value problem
with Dirichlet-Neumann mixed boundaries in a finite domain is
studied. The existence, uniqueness, and regularity of global
solutions are established with general large initial data in
$H^1$. It is proved that, although the solutions have large
oscillations, there is no shock wave, turbulence, vacuum, mass
concentration, or extremely hot spot developed in any finite time.

keywords:
global solutions
,
existence
,
real flows
,
reacting fluids
,
uniqueness
,
Combustion
,
a-priori estimates.

DCDS

A multidimensional piston problem for the Euler equations for compressible isentropic flow is analyzed.
Thepiston initially locates at the origin and experiences compressiveand expansive motions with spherical symmetry.
The initialsingularity at the origin is one of the difficulties for thisspherically symmetric piston problem.
A local shock front solutionfor the compressive motion is constructed based on thelinearization at
an approximate solution and the Newton iteration. A global entropy solution for the piston problem is
constructed byusing a shock capturing approach and the method of compensatedcompactness.

keywords:
entropy
,
compressive motion
,
origin.
,
expansive motion
,
piston problem
,
initial singularity
,
local solutions
,
Euler equations
,
global solutions

DCDS

The initial-boundary value problem for the equations of compressible viscoelastic flows is considered in a bounded domain of three-dimensional spatial dimensions.
The global existence of strong solution near equilibrium is established.
Uniform estimates in $W^{1,q}$ with $q>3$ on the
density and deformation gradient are also obtained.

KRM

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.

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