INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL

doi:10.1007/s10473-020-0215-5

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (2): 529-542.doi: 10.1007/s10473-020-0215-5

INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL

蒲学科¹, 郭柏灵²

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China

收稿日期:2018-12-29 修回日期:2019-04-16 出版日期:2020-04-25 发布日期:2020-05-26
作者简介:Xueke PU,E-mail:puxueke@gmail.com;Boling GUO,E-mail:gbl@iapcm.ac.cn
基金资助:
This article is support in part by NNSF (11871172) and Natural Science Foundation of Guangdong Province of China (2019A1515012000).

INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL

Xueke PU¹, Boling GUO²

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China

Received:2018-12-29 Revised:2019-04-16 Online:2020-04-25 Published:2020-05-26
Supported by:
This article is support in part by NNSF (11871172) and Natural Science Foundation of Guangdong Province of China (2019A1515012000).

摘要/Abstract

摘要： This article studies the initial-boundary value problem for a three dimensional magnetic-curvature-driven Rayleigh-Taylor model. We first obtain the global existence of weak solutions for the full model equation by employing the Galerkin's approximation method. Secondly, for a slightly simplified model, we show the existence and uniqueness of global strong solutions via the Banach's fixed point theorem and vanishing viscosity method.

关键词: Magnetic-curvature-driven Rayleigh-Taylor model, weak solutions, strong solutions, Banach fixed point theorem, vanishing viscosity method

Abstract: This article studies the initial-boundary value problem for a three dimensional magnetic-curvature-driven Rayleigh-Taylor model. We first obtain the global existence of weak solutions for the full model equation by employing the Galerkin's approximation method. Secondly, for a slightly simplified model, we show the existence and uniqueness of global strong solutions via the Banach's fixed point theorem and vanishing viscosity method.

Key words: Magnetic-curvature-driven Rayleigh-Taylor model, weak solutions, strong solutions, Banach fixed point theorem, vanishing viscosity method

中图分类号:

35K45

蒲学科, 郭柏灵. INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL[J]. 数学物理学报(英文版), 2020, 40(2): 529-542.

Xueke PU, Boling GUO. INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL[J]. Acta mathematica scientia,Series B, 2020, 40(2): 529-542.

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INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL

INITIAL BOUNDARY VALUE PROBLEM FOR THE 3D MAGNETIC-CURVATURE-DRIVEN RAYLEIGH-TAYLOR MODEL

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