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<p>In this paper we introduce two new classes of functional spaces, namely, Besov mixed-Morrey spaces and Fourier–Besov mixed-Morrey spaces, and then we establish some basic properties for these classes. Moreover, we explore the <i>d</i>-dimensional incompressible Navier–Stokes equations in this context, by a Bony’s paraproduct approach, in order to get the global well-posedness for small initial data. These results provide a new class of initial data with a sort of anisotropy in relation to its spatial variables or frequency variables.</p>

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Besov Mixed-Morrey Spaces: On an Application to the Navier–Stokes Equations

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  • 发表日期：

    2026年4月6日

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  • Leithold L. Aurazo-Alvarez,
  • Wladimir Neves

摘要

In this paper we introduce two new classes of functional spaces, namely, Besov mixed-Morrey spaces and Fourier–Besov mixed-Morrey spaces, and then we establish some basic properties for these classes. Moreover, we explore the d-dimensional incompressible Navier–Stokes equations in this context, by a Bony’s paraproduct approach, in order to get the global well-posedness for small initial data. These results provide a new class of initial data with a sort of anisotropy in relation to its spatial variables or frequency variables.