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April 17, 2026Mathematische Nachrichten0 citations

A Harnack‐Type Inequality for a Perturbed Singular Liouville Equation

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DBDaniele BartolucciUniversity of Rome Tor VergataPCP. CosentinoUniversity of Rome Tor VergataLWLina WuNanjing Normal University

Key Points

  • The aim is to establish a Harnack-type inequality for solutions of a perturbed Liouville equation influenced by turbulent flow dynamics.
  • Derived from Onsager's statistical mechanics framework.
  • Analyzed sequences of solutions in a bounded domain containing the origin.
  • Utilized mathematical techniques pertinent to singular equations.
  • Formulated a specific Harnack-type inequality relevant to the perturbed Liouville equation.
  • Established conditions under which this inequality holds.
  • Highlighted the relevance of the results to analyzing turbulent Euler flows.

Abstract

ABSTRACT Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we obtain a Harnack‐type inequality for sequences of solutions of the following perturbed Liouville equation, where , , is a bounded domain in containing the origin and satisfies

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Cite This Study

Bartolucci et al. (2026) studied this question.

synapsesocial.com/papers/69e1cfcb5cdc762e9d858bbchttps://doi.org/10.1002/mana.70149
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