论文标题
液体动力学的保守数量和规律性
Conserved quantities and regularity in fluid dynamics
论文作者
论文摘要
保守或消散数量（例如能量或熵）是许多与流体力学有关的时间依赖性PDE的研究的核心。例如，对于欧拉（Euler）和纳维尔（Navier-Stokes）方程，保护法和运输方程式就是这种情况。在所有这些情况下，正式保守的数量可能不再是较低的溶液的时间恒定的。规律性与保护数量之间的微妙相互作用涉及二型二角狮式传输和连续性方程理论中的重新量量相关，以及在理想不可压缩流体的领域中的Onsager的猜想。我们将回顾Diperna-Lions和Constantin-e-Titi的经典换向器方法，然后取得更新的结果。
Conserved or dissipated quantities, like energy or entropy, are at the heart of the study of many classes of time-dependent PDEs in connection with fluid mechanics. This is the case, for instance, for the Euler and Navier-Stokes equations, for systems of conservation laws, and for transport equations. In all these cases, a formally conserved quantity may no longer be constant in time for a weak solution at low regularity. The delicate interplay between regularity and conservation of the respective quantity relates to renormalisation in the DiPerna-Lions theory of transport and continuity equations, and to Onsager's conjecture in the realm of ideal incompressible fluids. We will review the classical commutator methods of DiPerna-Lions and Constantin-E-Titi, and then proceed to more recent results.
