三维不可压MHD方程在变指数Lebesgue空间中的适定性
Well-Posedness for 3D Incompressible MHD Equations in Lebesgue Spaces with Variable Exponents
DOI: 10.12677/aam.2024.135220, PDF,    国家自然科学基金支持
作者: 陈 浩, 赵继红*：宝鸡文理学院数学与信息科学学院，陕西 宝鸡
关键词: MHD方程；变指数Lebesgue空间；适定性；MHD Equations； Lebesgue Spaces with Variable Exponents； Well-Posedness
摘要: 该文主要考虑了三维不可压MHD方程在变指数Lebesgue空间中的适定性。通过克服变指数Lebesgue空间与经典的Lebesgue空间不同所带来的困难，建立了三维不可压MHD方程在空间ℒ3p(⋅)(ℝ3,L∞(0,∞))中小初值问题的整体适定性，并在空间Lp(⋅)([0,T],Lq(ℝ3))中证明了大初值问题的局部适定性。
Abstract: In this paper, we are mainly concerned with the well-posedness of the 3D incompressible MHD equations in Lebesgue spaces with variable exponents. By overcoming some difficulties caused by the differences between the Lebesgue spaces with variable exponents and the usual one, we establish, for the 3D incompressible MHD equations, the global well-posedness in spaceℒ3p(⋅)(ℝ3,L∞(0,∞))with small initial data, and the local well-posedness inLp(⋅)([0,T],Lq(ℝ3))with general initial data.
文章引用：陈浩, 赵继红. 三维不可压MHD方程在变指数Lebesgue空间中的适定性[J]. 应用数学进展, 2024, 13(5): 2331-2341. https://doi.org/10.12677/aam.2024.135220

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