Estimates of Mild Solutions of Navier–Stokes Equations in Weak Herz-Type Besov–Morrey Spaces

Ruslan Abdulkadirov and Pavel Lyakhov
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Ruslan Abdulkadirov: North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355009 Stavropol, Russia
Pavel Lyakhov: Department of Automation and Control Processes, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia

Mathematics, 2022, vol. 10, issue 5, 1-13

Abstract: The main goal of this article is to provide estimates of mild solutions of Navier–Stokes equations with arbitrary external forces in R n for n ≥ 2 on proposed weak Herz-type Besov–Morrey spaces. These spaces are larger than known Besov–Morrey and Herz spaces considered in known works on Navier–Stokes equations. Morrey–Sobolev and Besov–Morrey spaces based on weak-Herz space denoted as W K ˙ p , q α M μ s and W K ˙ p , q α N ˙ μ , r s , respectively, represent new properties and interpolations. This class of spaces and its developed properties could also be employed to study elliptic, parabolic, and conservation-law type PDEs.

Keywords: system of PDEs; function spaces; mild solutions; real interpolation; heat semigroup operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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