GLOBAL SOLUTION FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH A CLASS OF LARGE DATA IN $ BMO^{-1}(\mathbb{R}^3) $

Congchong Guo

doi:10.11948/20250371

2026 Volume 16 Issue 4

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Congchong Guo. GLOBAL SOLUTION FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH A CLASS OF LARGE DATA IN $ BMO^{-1}(\mathbb{R}^3) $[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2154-2171. doi: 10.11948/20250371

Citation:

Congchong Guo. GLOBAL SOLUTION FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH A CLASS OF LARGE DATA IN $ BMO^{-1}(\mathbb{R}^3) $[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2154-2171. doi: 10.11948/20250371

GLOBAL SOLUTION FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH A CLASS OF LARGE DATA IN $ BMO^{-1}(\mathbb{R}^3) $

Congchong Guo^1, ,

1.
College of Information Engineering, Longyan University, Dongxiao Street, 364012 Longyan, China

Corresponding author: Email: guocongchong77@163.com(C. Guo)
Fund Project: The authors were supported by National Natural Science Foundation of China (11971199) and Fujian Provincial Youth Innovation Project (2019J05115)

Abstract

Abstract

In [12], Koch & Tataru have proved the global well-posedness of the Navier-Stokes equations with small initial data $ u_0 \in BMO^{-1}(\mathbb{R}^n) $, and then the spatial and time analyticity of the Koch & Tataru solution have been presented by Germain-Pavlovć-Stffilani [9] and the first author [3] when the initial data $ u_0 \in BMO^{-1}(\mathbb{R}^n) $ small enough. Subsequently, the similar results for the incompressible MHD equations have been studied by the first author [4] for $ (u_0,b_0)\in BMO^{-1}(\mathbb{R}^n) $ small enough. In this paper, we shall prove the global well-posedness for the incompressible MHD equations with a class of large data $ (u_0,b_0)\in BMO^{-1}(\mathbb{R}^n) $. Besides, the space-time regularities also have been proved.
- Global regularity /
- MHD equations /
- large data /
- Koch-Tataru solution
MSC: 35Q35, 76W05, 35B65, 42B35

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References

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