Global well-posedness of the incompressible fractional Navier–Stokes equations in Fourier–Besov spaces with variable exponents. (15th February 2019)

• Record Type: Journal Article
• Authors: Ru, Shaolei; Abidin, Muhammad Zainul
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 4(2019)
• Page Start: 1082
• Page End: 1090
• Publication Date: 2019-02-15
• Subjects: Fractional Navier–Stokes equations -- Variable exponent Fourier–Besov spaces -- Global well-posedness; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.10.039
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We study the Cauchy problem of the fractional Navier–Stokes equations in critical variable exponent Fourier–Besov spaces F B ̇ p ( ⋅ ), q 4 − 2 α − 3 p ( ⋅ ) . We discuss some properties of variable exponent Fourier–Besov spaces and prove a general global well-posedness result which covers some recent works about classical Navier–Stokes equations.