TY - JOUR
T1 - Local Well-Posedness of the Three Dimensional Linearized MHD Boundary Layer System
AU - Chen , Ke
AU - Li , Wei-Xi
AU - Yang , Tong
JO - Communications in Mathematical Analysis and Applications
VL - 4
SP - 483
EP - 500
PY - 2024
DA - 2024/12
SN - 3
DO - http://doi.org/10.4208/cmaa.2024-0020
UR - https://global-sci.org/intro/article_detail/cmaa/23615.html
KW - Well-posedness theory, cancellation mechanism, MHD boundary layer, structural assumptions.
AB - <p style="text-align: justify;">For the three dimensional linearized MHD boundary layer system
around a shear flow, we establish a well-posedness result with Sobolev regularity in one tangential direction under the non-degeneracy condition in that
direction. The proof is based on an observation of a new cancellation mechanism that is different from the two space dimensional case. Precisely, the
new cancellation relies on the evolution of the magnetic field orthogonal to the
boundary instead of the stream function in two space dimension. Even though
this kind of cancellation can help to lower the regularity requirement in only
one tangential direction while analyticity is still needed in the other tangential direction, we expect that this can be viewed as one step further to study
the challenging problem on the well-posedness theory in Sobolev space of the
three dimensional MHD boundary layer system under some suitable structural
assumption.</p>