单原子气体方程的哪些测度值解是由弱解生成的？
Which measure-valued solutions of the monoatomic gas equations are generated by weak solutions?
摘要：
与不可压缩情形相反，可压缩欧拉方程的每一个测度值解并不是都能由弱解或粘性序列的消失产生的。本文给出了等熵Euler方程组的容许测度值解由弱解生成的充分条件。作为关键步骤之一，我们证明了Fonseca和Müller的刻画结果的$L^{\infty}$ -变体，以生成$\mathcal{A}$ -free Young测度。更具体的版本，我们的结果的情况下，由两个狄拉克措施的解决方案。最后，我们还讨论了必要条件产生的测度值的解决方案由弱解或消失的粘性序列，并会指出，所产生的差距主要是由于获得唯一的统一$L^p$ -界的$1<p<\infty$，而不是$p=\infty$。
英文摘要：
Contrary to the incompressible case not every measure-valued solution of the compressible Euler equations can be generated by weak solutions or a vanishing viscosity sequence. In the present paper we give sufficient conditions on an admissible measure-valued solution of the isentropic Euler system to be generated by weak solutions. As one of the crucial steps we prove an $L^{\infty}$-variant of Fonseca and Müller's characterization result for generating $\mathcal{A}$-free Young measures in terms of potential operators. More concrete versions of our results are presented in the case of a solution consisting of two Dirac measures. We conclude by discussing also necessary conditions for generating a measure-valued solution by weak solutions or a vanishing viscosity sequence and will point out that the resulting gap mainly results from obtaining only uniform $L^p$-bounds for $1<p<\infty$ instead of $p=\infty$.
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