Scholarlink

<p>In this paper, we are concerned with the well-posed issues of the fractional dissipative system in the framework of the Fourier–Besov spaces with variable regularity and integrability indices. By fully using some basic properties of these variable function spaces, we establish the linear estimates in variable Fourier–Besov spaces for the fractional heat equation. Such estimates are fundamental for solving certain dissipative PDE’s of fractional type. As an applications, we prove global well-posedness in variable Fourier–Besov spaces for the 3D generalized incompressible Navier–Stokes equations and the 3D fractional Keller–Segel system.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Global Well-Posedness of the Fractional Dissipative System in the Framework of Variable Fourier–Besov Spaces

  • 期刊论文

  • 发表日期：

    2025年8月11日

查看全文
  • Gastón Vergara-Hermosilla,
  • Jihong Zhao

摘要

In this paper, we are concerned with the well-posed issues of the fractional dissipative system in the framework of the Fourier–Besov spaces with variable regularity and integrability indices. By fully using some basic properties of these variable function spaces, we establish the linear estimates in variable Fourier–Besov spaces for the fractional heat equation. Such estimates are fundamental for solving certain dissipative PDE’s of fractional type. As an applications, we prove global well-posedness in variable Fourier–Besov spaces for the 3D generalized incompressible Navier–Stokes equations and the 3D fractional Keller–Segel system.