What question did this study set out to answer?

To establish the global well-posedness of incompressible magnetohydrodynamics (MHD) equations with large initial data.

March 25, 2026Open Access

GLOBAL SOLUTION FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH A CLASS OF LARGE DATA IN BMO^-1 (R³)

Puntos clave

To establish the global well-posedness of incompressible magnetohydrodynamics (MHD) equations with large initial data.
Proved global well-posedness for large data $(u_0,b_0) \in BMO^{-1}(\mathbb{R}^n)$
Validated space-time regularity of solutions
Built on prior work for small initial data
Confirmed global well-posedness for the incompressible MHD equations with large data
Demonstrated space-time regularity for the solutions

Resumen

In 12, Koch & Tataru have proved the global well-posedness of the Navier-Stokes equations with small initial data u₀ BMO^-1 (Rⁿ), 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 u₀ BMO^-1 (Rⁿ) small enough. Subsequently, the similar results for the incompressible MHD equations have been studied by the first author 4 for (u₀, b₀) BMO^-1 (Rⁿ) small enough. In this paper, we shall prove the global well-posedness for the incompressible MHD equations with a class of large data (u₀, b₀) BMO^-1 (Rⁿ). Besides, the space-time regularities also have been proved.

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