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<p>In this paper, we study Lagrangian flows and their induced Lagrangian solutions associated to very singular vector fields. More precisely, we provide a simplified proof of&#xa0;Nguyen Q-H (Commun Pure Appl Math&#xa0;74:1129–1192, 2021) of existence, uniqueness and semigroup property for Lagrangian flows for vector fields defined as a convolution of an appropriate regular function and a non Calder n-Zygmund singular kernel, that is, a function whose singularity at the origin is different than the classical one.</p>

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Lagrangian Flow for Very Singular Integral Vector Fields and Application for Generalized SQG Equation

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Henrique Borrin

摘要

In this paper, we study Lagrangian flows and their induced Lagrangian solutions associated to very singular vector fields. More precisely, we provide a simplified proof of Nguyen Q-H (Commun Pure Appl Math 74:1129–1192, 2021) of existence, uniqueness and semigroup property for Lagrangian flows for vector fields defined as a convolution of an appropriate regular function and a non Calder n-Zygmund singular kernel, that is, a function whose singularity at the origin is different than the classical one.