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A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2021-04-29 , DOI: 10.1137/19m1283938 Chenyun Luo , Junyan Zhang
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2021-04-29 , DOI: 10.1137/19m1283938 Chenyun Luo , Junyan Zhang
SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2595-2630, January 2021.
We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on the boundary. We establish an priori estimate for solutions in the Lagrangian coordinates with $H^{3.5}$ regularity. To the best of our knowledge, this is the first result focusing on the incompressible ideal free-boundary MHD equations with surface tension. It is worth pointing out that the $1/2$-extra spatial regularity for the flow map $\eta$, such as in [T. Alazard, N. Burq, and C. Zuily, Invent. Math., 198 (2014), pp. 71--163; I. Kukavica, A. Tuffaha, and V. Vicol, Appl. Math. Optim., 76 (2017), pp. 535--563; C. Luo and J. Zhang, Nonlinearity, 33 (2020), pp. 1499--1527], is no longer required in this manuscript thanks to the presence of the surface tension on the boundary.
中文翻译：
具有表面张力的不可压缩自由边界磁流体动力学方程的先验估计
SIAM数学分析杂志，第53卷，第2期，第2595-2630页，2021年1月。
我们考虑边界域中具有表面张力的三维不可压缩自由边界磁流体动力学（MHD）方程。我们以规则性$ H ^ {3.5} $在拉格朗日坐标中建立解决方案的先验估计。据我们所知，这是第一个关注表面张力不可压缩的理想自由边界MHD方程的结果。值得指出的是，流图$ \ eta $的$ 1/2 $额外的空间规律性，例如[T. N. Burq的Alazard和C.Zuily的发明。《数学》 198（2014），第71--163页; I.Kukavica，A.Tuffaha和V.Vicol，Appl。数学。Optim。，76（2017），第535--563页; C. Luo和J. Zhang，Nonlinearity，33（2020），pp。1499--1527]，由于边界上存在表面张力，因此在本手稿中不再需要。
更新日期：2021-04-30
We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on the boundary. We establish an priori estimate for solutions in the Lagrangian coordinates with $H^{3.5}$ regularity. To the best of our knowledge, this is the first result focusing on the incompressible ideal free-boundary MHD equations with surface tension. It is worth pointing out that the $1/2$-extra spatial regularity for the flow map $\eta$, such as in [T. Alazard, N. Burq, and C. Zuily, Invent. Math., 198 (2014), pp. 71--163; I. Kukavica, A. Tuffaha, and V. Vicol, Appl. Math. Optim., 76 (2017), pp. 535--563; C. Luo and J. Zhang, Nonlinearity, 33 (2020), pp. 1499--1527], is no longer required in this manuscript thanks to the presence of the surface tension on the boundary.
中文翻译：
具有表面张力的不可压缩自由边界磁流体动力学方程的先验估计
SIAM数学分析杂志，第53卷，第2期，第2595-2630页，2021年1月。
我们考虑边界域中具有表面张力的三维不可压缩自由边界磁流体动力学（MHD）方程。我们以规则性$ H ^ {3.5} $在拉格朗日坐标中建立解决方案的先验估计。据我们所知，这是第一个关注表面张力不可压缩的理想自由边界MHD方程的结果。值得指出的是，流图$ \ eta $的$ 1/2 $额外的空间规律性，例如[T. N. Burq的Alazard和C.Zuily的发明。《数学》 198（2014），第71--163页; I.Kukavica，A.Tuffaha和V.Vicol，Appl。数学。Optim。，76（2017），第535--563页; C. Luo和J. Zhang，Nonlinearity，33（2020），pp。1499--1527]，由于边界上存在表面张力，因此在本手稿中不再需要。
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