Isentropic Approximation of Quasi-One-Dimensional Unsteady Nozzle Flow

For the quasi–one-dimensional unsteady nozzle flow under the assumptions that both the initial data and the area of varying cross-sections have sufficiently small total variation, we proved that in any bounded domain the $L^1$ norm of the difference between solutions of isentropic and non-isentropic balance laws with the same initial data can be bounded by the cube of the total variation of the initial data and the area of varying cross-sections.

[1]  Tai-Ping Liu.  Nonlinear stability and instability of transonic flows through a nozzle , 1982 .

[2]  Gui-Qiang G. Chen,et al.  Dependence of entropy solutions in the large for the euler equations on nonlinear flux functions , 2007 .

[3]  S. Bianchini,et al.  On the stability of the standard Riemann semigroup , 2000, math/0007055.

[4]  G. Guerra,et al.  Global BV Entropy Solutions and Uniqueness for Hyperbolic Systems of Balance Laws , 2002 .

[5]  Tai-Ping Liu.  Transonic gas flow in a duct of varying area , 1982 .

[6]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[7]  A. Majda.  Compressible fluid flow and systems of conservation laws in several space variables , 1984 .

[8]  James Glimm,et al.  A generalized Riemann problem for quasi-one-dimensional gas flows , 1984 .

[9]  P. Lax.  Hyperbolic systems of conservation laws II , 1957 .

[10]  A. Bressan.  Hyperbolic systems of conservation laws : the one-dimensional Cauchy problem , 2000 .

[11]  Gui-Qiang G. Chen,et al.  Continuous Dependence of Entropy Solutions to the Euler Equations on the Adiabatic Exponent and Mach Number , 2008 .

[12]  L. Saint-Raymond.  Isentropic Approximation¶of the Compressible Euler System¶in One Space Dimension , 2000 .

[13]  John M. Hong.  An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by “weaker than weak” solutions of the Riemann problem , 2006 .

[14]  Yongqian Zhang.  On the irrotational approximation to steady supersonic flow , 2007 .

[15]  J. Glimm.  Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .

[16]  Andrew J. Majda,et al.  One Perspective on Open Problems in Multi-Dimensional Conservation Laws , 1991 .

[17]  C. M. Dafermos,et al.  Hyberbolic [i.e. Hyperbolic] conservation laws in continuum physics , 2005 .

[18]  Tai-Ping Liu.  Quasilinear hyperbolic systems , 1979 .