摘要
The vanishing pressure limit of continuous solutions isentropic Euler equations is analyzed, which is formulated as small parameter epsilon goes to 0. Due to the characteristics being degenerated in the limiting process, the resonance may cause the mass concentration. It is shown that in the pressure vanishing process, for the isentropic Euler equations, the continuous solutions with compressive initial data converge to the mass concentration solution of pressureless Euler equations, and with rarefaction initial data converge to the continuous solutions globally. It is worth to point out: u converges in C-1, while rho converges in C-0, due to the structure of pressureless Euler equations. To handle the blow-up of density p and spatial derivatives of velocity u, a new level set argument is introduced. Furthermore, we consider the convergence rate with respect to e, both u and the area, of characteristic triangle are a order, while the rates of rho and u(x) depend on the further regularity of the initial data of u.
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单位武汉理工大学