A pde with drift of negative Besov index and linear growth solutions

2022/12/08 by Elena Issoglio, Issoglio, Elena, Francesco Paolo Russo +1
Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2212.04293

openalex publication_date 2022/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates a class of PDEs with coefficients in negative Besov spaces and whose solutions have linear growth. We show existence and uniqueness of mild and weak solutions, which are equivalent in this setting, and several continuity results. To this aim, we introduce ad-hoc Besov-Hölder type spaces that allow for linear growth, and investigate the action of the heat semigroup on them. We conclude the paper by introducing a special subclass of these spaces which has the useful property to be separable.

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