论文标题
等温方程的等温限制等等激素动力学
Isothermal Limit of Entropy Solutions of the Euler Equations for Isentropic Gas Dynamics
论文作者
论文摘要
我们关注$ l^\ infty $中的熵解决方案的等温限制，包含真空状态的等激气方程。我们证明，当绝热指数$γ\ rightArrow 1 $时，等速Euler方程的$ l^\ Infty $中的熵解决方案强烈收敛到等温欧拉方程的相应熵解决方案。这是通过将仔细的熵分析和精制动力学配方与补偿紧凑性论证相结合以获得限制所需的均匀估计值来实现的。熵分析涉及仔细估计当绝热指数$γ\ to 1 $时，等于等温的欧拉方程相应的熵对之间的关系。精制了具有均匀界限初始数据的等等晶体方程的熵溶液的动力学公式，因此，配方中耗散度量的总变化相对于$γ> 1 $在局部均匀界定。还提供了包含真空状态的Riemann溶液的显式渐近分析。
We are concerned with the isothermal limit of entropy solutions in $L^\infty$, containing the vacuum states, of the Euler equations for isentropic gas dynamics. We prove that the entropy solutions in $L^\infty$ of the isentropic Euler equations converge strongly to the corresponding entropy solutions of the isothermal Euler equations, when the adiabatic exponent $γ\rightarrow 1$. This is achieved by combining careful entropy analysis and refined kinetic formulation with compensated compactness argument to obtain the required uniform estimates for the limit. The entropy analysis involves careful estimates for the relation between the corresponding entropy pairs for the isentropic and isothermal Euler equations when the adiabatic exponent $γ\to 1$. The kinetic formulation for the entropy solutions of the isentropic Euler equations with the uniformly bounded initial data is refined, so that the total variation of the dissipation measures in the formulation is locally uniformly bounded with respect to $γ>1$. The explicit asymptotic analysis of the Riemann solutions containing the vacuum states is also presented.
