AI 中文总结
该研究针对欧拉方程的凸积分扇形解，推导了相关熵率与作用率的显式表达式，刻画了Dafermos熵率准则与作用率准则的一致性，通过精确算术计算验证了两种准则均偏好凸积分解。
AI 中文摘要
对于等熵欧拉方程的一般分段常数扇形亚解，相对于共同参考解，任意相关凸积分解的熵率和作用率的显式计算表明，这些率仅依赖于扇形。此外，这些显式表达式可分解为动能失配和内能失配，由此我们刻画了Dafermos熵率准则与作用率准则的一致性。我们将此应用于Krupa和Székelyhidi构造的黎曼数据解，其经典解为平面接触间断。经认证的精确算术计算显示，在两两比较中，两种准则均偏好凸积分解而非经典自相似解。
英文摘要
For piecewise constant fan subsolutions to the isentropic Euler equations, the entropy and action rates of any associated convex integration solution, relative to a common reference solution, depend only on the fan and are computed explicitly. Moreover, these explicit expressions may be decomposed into a kinetic energy mismatch and an internal energy mismatch, from which we characterize agreement of Dafermos' entropy rate criterion with action rate criteria. The known disagreement for the Chiodaroli--Kreml two-shock data is recovered. For the planar contact reference, we prove that both criteria strictly prefer every convex integration solution associated with a strictly dissipative admissible fan to the classical contact discontinuity. Certified computations locate the Krupa--Székelyhidi solutions in this region, where the criteria agree, while Horimoto's analytical construction provides such fans for every strictly increasing pressure law.
Comments27 pages, new Theorem 4.3
