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Mathematics > History and Overview

arXiv:2211.03159 (math)
[Submitted on 6 Nov 2022]

Title:Can probability theory really help tame problems in mathematical hydrodynamics?

Authors:Martina Hofmanová, Florian Bechtold
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Abstract: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.
Subjects: History and Overview (math.HO); Analysis of PDEs (math.AP); Probability (math.PR)
Cite as: arXiv:2211.03159 [math.HO]
  (or arXiv:2211.03159v1 [math.HO] for this version)
  https://doi.org/10.48550/arXiv.2211.03159

Submission history

From: Florian Bechtold [view email]
[v1] Sun, 6 Nov 2022 15:55:54 UTC (22 KB)
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