Renhui Wan
Abstract:
In this article, we consider the tridimensional generalized
Hall magneto-hydrodynamics (Hall-MHD) system,
with
and
.
For
,
,
we obtain the global regularity of classical solutions.
For
and
,
with small data,
the system also possesses global classical solutions. In addition,
for the standard Hall-MHD system,
,
by adding a suitable condition, we give a positive answer to the open
question in [3].
At last, we study the regularity criterions of generalized Hall-MHD system.
In particular, we prove the regularity criterion in terms of horizontal
gradient
for
,
.
Submitted November 11, 2014. Published June 29, 2015.
Math Subject Classifications: 35Q35, 35B65, 76W05.
Key Words: Generalized Hall-mhd system; global regularity; classical solutions.
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Renhui Wan Department of mahtematics Zhejiang University Hangzhou, Zhejiang 310027, China email: rhwanmath@zju.edu.cn, rhwanmath@163.com |
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