论文标题
概率理论能否真正有助于驯服数学流体动力学中的问题？
Can probability theory really help tame problems in mathematical hydrodynamics?
论文作者
论文摘要
近年来，在流体动力方程的数学研究中取得了惊人的进步。尤其是凸集成的新工具在建立非唯一性结果方面证明了极具用途。在确定性环境中解决方案的这种“病理”行为的动机，流体动力学的随机模型从数学界越来越兴趣。受“噪声正规化”理论的启发，希望这种随机性可能有助于避免“病理学”，例如弱解决方案的非唯一性。然而，当前的研究表明，即使有随机的扰动，凸集成方法也可以占上风。
Recent years have seen spectacular progress in the mathematical study of hydrodynamic equations. Novel tools from convex integration in particular prove extremely versatile in establishing non-uniqueness results. Motivated by this 'pathological' behavior of solutions in the deterministic setting, stochastic models of fluid dynamics have enjoyed growing interest from the mathematical community. Inspired by the theory of 'regularization by noise', it is hoped for that stochasticity might help avoid 'pathologies' such as non-uniqueness of weak solutions. Current research however shows that convex integration methods can prevail even in spite of random perturbations.
