摘要
在速度梯度和磁场梯度满足一定的衰减性,且初始总动量非零的条件下,研究了全空间三维等熵可压缩磁流体方程在有限时间内经典解的爆破现象。通过构造球体证明质量、动量和能量在全空间守恒,并在此基础上使用Hölder不等式、插值不等式等方法处理相关非线性项,得到了爆破现象。
Under the conditions that the gradient of the velocity and magnetic field satisfy a certain decay,and the initial total momentum does not vanish,the explosion phenomenon of classical solutions of the three-dimensional isentropic compressible magnetohydrodynamic equation in finite time is studied.Blow-up result is derived by constructing the sphere to prove the conservation of mass,momentum and energy in full space and applying Hölder inequality,interpolation inequalities,and other methods to deal with relevant nonlinear terms.
作者
丁熙来
李金泽
DING Xilai;LI Jinze(College of Mathematical Sciences,Yangzhou University,Yangzhou Jiangsu 225002)
出处
《首都师范大学学报(自然科学版)》
2025年第6期49-53,共5页
Journal of Capital Normal University:Natural Science Edition
基金
江苏高校品牌专业建设工程项目(PPZY2015B109)
江苏省自然科学基金项目(BK20221369)。
关键词
微分方程
爆破
等熵
可压缩磁流体方程
经典解
Hölder不等式
differential equation
blow-up
isentropic
compressible magnetohydrodynamics
classical solutions
Hölder inequality
