An Improved Blow-Up Criterion for the Magnetohydrodynamics with the Hall and Ion-Slip Effects

In this work, we consider the magnetohydrodynamics system with the Hall and ion-slip effects in ℝ3. The main result is a sufficient condition for regularity on a time interval [0, T] expressed in terms of the norm of the homogeneous Besov space $${\dot{B}}_{\infty ,\infty }^{0}$$ with respect to the pressure and the BMO−norm with respect to the gradient of the magnetic field, respectively $$\underset{0}{\overset{T}{\int }}\left({\Vert abla \pi \left(t\right)\Vert }_{{\dot{B}}_{\infty ,\infty }^{0}}^\frac{2}{3}+{\Vert abla B\left(t\right)\Vert }_{BMO}^{2}\right)dt<\infty ,$$ which can be regarded as improvement of the result in [3].

Авторы
Gala S.1, 2 , Ragusa M.A. 2, 3
Издательство
Springer New York LLC
Номер выпуска
2
Язык
Английский
Страницы
306-313
Статус
Опубликовано
Том
278
Год
2024
Организации
  • 1 Ecole Normale Supérieure of Mostaganem
  • 2 Università di Catania
  • 3 RUDN University
Ключевые слова
magnetohydrodynamics system; hall effect; ion-slip effect; homogeneous Besov space; blow-up criterion; mathematics; general
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