On the cauchy problem to the system of one-dimensional isentropic/isothermal in compressible flow^*

^*project supported by NNSFC

Abstract

This paper considers the Cauchy problem to the system of one-dimensional isentropic/isothermal compressible flow

where ε; 0 is a constant, is the adiabatic exponent. A global existence result with large initial data is established by employing Chueh, Conley, and smoller's theory of positively invariant regions, the method of energy integral, and some delicate estimates.

Keywords:

• One-dimensional isentropic/isothermal compressible flow
• theory of positively invariant regions
• the method of energy integral

^*project supported by NNSFC

^*project supported by NNSFC

Notes

^*project supported by NNSFC