Work

The mild solution of the inhomogeneous fractional incompressible Navier-Stokes equation on $ \mathbb{R}^n $

Year: 2025

Type: article

Abstract: In this paper, we study the existence of local and global mild solutions for a nonhomogeneous fractional incompressible Navier-Stokes system when initial values belong to subcritical and critical Lebesgue spaces. With the help of the pointwise estimates of the fractional heat kernel, the corresponding bilinear operator estimates have been established for subcritical case. However, it is unbounded in the critical Banach space $ C(0,+\infty; L^{\frac{n}{2\alpha-1}}( \mathbb{R}^n)) $. To get rid of this difficulty, we consider a subspace of $ C(0,+\infty; L^{\frac{n}{2\alpha-1}}( \mathbb{R}^n)) $ which enables us to obtain the related bilinear operator estimates. Based on these bilinear operator estimates, the existence of local and global mild solutions of nonhomogeneous fractional incompressible Navier-Stokes equations are established.

Source: Discrete and Continuous Dynamical Systems - B

DOI: 10.3934/dcdsb.2025103

Authors: Ge Tang, Shuke Xu

Institutions: Hunan Normal University, Henan University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, National Natural Science Foundation of China

Award: G2345990001