This paper concerns the global existence of solutions in for the nonlinear compressible Navier–Stokes equations of an initial-boundary value problem with an external force and a heat source. Some important inequalities are used and some new results are obtained.
REFERENCES
1.
Cho
, Y.
, Choe
, H. J.
, and Kim
, H.
, “Unique solvability of the initial boundary value problems for compressible viscous fluids
,” J. Math. Pures Appl.
83
, 243
–275
(2004
).2.
Fujita-Yashima
, H.
and Benabidallah
, R.
, “Unicité de la solution de l’équation menodimensionnelle oua’ symétrie sphérique d’un gaz visqueux calorifére
,” Rend. Circ. Mat. Palermo
42
, 195
–218
(1993
).3.
Fujita-Yashima
, H.
and Benabidallah
, R.
, “Equation a’symétrie sphérique d’un gaz visqueux et caloeifére avec la surface libre
,” Ann. Mat. Pura Appl.
168
, 75
–117
(1995
).4.
Jiang
, S.
, “Large-time behavior of solutions to the equations of a viscous polytropic ideal gas
,” Ann. Mat. Pura Appl.
CLXXV
, 253
–275
(1998
).5.
Qin
, Y.
, “Global existence and asymptotic behavior for a viscous, heat-conductive, one-dimensional real gas with fixed and thermally insulated endpoints
,” Nonlinear Anal. Theory, Methods Appl.
44
, 413
–441
(2001
).6.
Qin
, Y.
, “Global existence and asymptotic behavior of solutions to the system in one-dimensional nonlinear thermoviscoelasticity
,” Q. Appl. Math.
59
, 113
–142
(2001
).7.
Qin
, Y.
, “Global existence and asymptotic behavior for a viscous, heat-conductive, one-dimensional real gas with fixed and constant temperature boundary conditions
,” Adv. Differ. Equ.
7
, 129
–154
(2002
).8.
Qin
, Y.
, “Exponential stability for a nonlinear one-dimensional heat-conducting viscous real gas
,” J. Math. Anal. Appl.
272
, 507
–535
(2002
).9.
Qin
, Y.
, “Universal attractor in for the nonlinear one-dimensional compressible Navier-Stokes equations
,” J. Differ. Equations
207
, 21
–72
(2004
).10.
Qin
, Y.
, “Exponential stability for the compressible Navier-Stokes equations with the cylinder symmetry in
,” IMA J. Appl. Math.
70
, 1
–18
(2005
).11.
Qin
, Y.
, Ma
, T. F.
, Cavalcanti
, M. M.
, and Andrade
, D.
“Exponential stability in for the Navier-Stokes equations of compressible and heat conductive fluid
,” Commun. Pure Appl. Anal.
4
, 635
–664
(2005
).12.
Qin
, Y.
and Muńoz Rivera
, J. E.
, “Global existence and exponential stability in one-dimensional nonlinear thermoelasticity with thermal memory
,” Nonlinear Anal. Theory, Methods Appl.
51
, 11
–32
(2002
).13.
Qin
, Y.
and Muńoz Rivera
, J. E.
, “Large-time behaviour of energy in elasticity
,” J. Elast.
66
, 171
–184
(2002
).14.
Qin
, Y.
and Mu’noz Rivera
, J. E.
, “Polynomial Decay for the Energy with an Acoustic Boundary Condition
, Appl. Math. Lett.
16
, 249
–256
(2003
).15.
Qin
, Y.
and Muńoz Rivera
, J. E.
, “Global existence and exponential stability of solutions to thermoelastic equations of hyperbolic type
,” J. Elast.
5
, 125
–145
(2005
).16.
Xu
, C.-J.
and Yang
, T.
, “Local existence with physical vacuum boundary condition to Euler equations with damping
,” J. Differ. Equations
210
, 217
–231
(2005
).17.
Yanagi
, S.
, “Existence of periodic solutions for a one-dimensional isentropic model system of compressible viscous gas
,” Nonlinear Anal. Theory, Methods Appl.
46
, 279
–298
(2001
).18.
Zheng
, S.
, Nonlinear Evolution Equations
, Pitman Monographs and Surveys in Pure and Applied Mathematics
Vol. 133
(CRC
, Boca Raton, FL
, 2004
).19.
Zheng
, S.
and Qin
, Y.
, “Universal attractors for the Navier-Stokes equations of compressible and heat-conductive fluid in bounded annular domains in
,” Arch. Ration. Mech. Anal.
160
, 153
–179
(2001
).20.
Zimmer
, J.
, “Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy
, J. Math. Anal. Appl.
292
, 589
–604
(2004
).© 2008 American Institute of Physics.
2008
American Institute of Physics
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