【摘要】：本文的主要研究3維不可壓MHD(Magnetohydrodynamic)方程強(qiáng)解的整體存在性及應(yīng)用時(shí)間分段估計(jì)的方法研究帶有大外力的3維不可壓MHD方程強(qiáng)解的整體存在性。全文分成以下三部分,即:第一部分:介紹3維不可壓MHD方程強(qiáng)解的研究背景、研究現(xiàn)狀以及進(jìn)行證明所用到一些重要理論和不等式等基本知識(shí)。第二部分:研究3維不可壓MHD方程強(qiáng)解的整體存在性的問(wèn)題,在Kim和Craig等等研究成果的基礎(chǔ)上,在不弱化小初值條件下,通過(guò)使方程的質(zhì)量或者密度適當(dāng)小時(shí)或粘性系數(shù)足夠大時(shí),從而得到方程存在整體強(qiáng)解。第三部分:研究3維不可壓MHD方程在帶有大外力的情況下強(qiáng)解的存在性問(wèn)題,在前人已證明3維不可壓MHD方程強(qiáng)解局部存在性的研究成果上,結(jié)合時(shí)間分段估計(jì)證明方法,從而得到帶有大外力的3維不可壓MHD方程強(qiáng)解的整體存在性。
[Abstract]:In this paper, we mainly study the global existence of strong solutions for 3-dimensional incompressible MHD (Magnetohydrodynamic) equations and the global existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces by using the method of time piecewise estimation. The full text is divided into the following three parts: in the first part, the research background, research status and some important theories and inequalities used to prove the strong solution of three-dimensional incompressible MHD equation are introduced. In the second part, we study the global existence of strong solutions for 3-dimensional incompressible MHD equations. on the basis of Kim and Craig's research results, without weakening the small initial value, By making the mass or density of the equation small enough or when the viscosity coefficient is large enough, the global strong solution of the equation is obtained. In the third part, the existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces is studied. on the basis of the previous research results on the local existence of strong solutions for 3-dimensional incompressible MHD equations, combined with the time piecewise estimation method, Thus, the global existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces is obtained.
【學(xué)位授予單位】：華僑大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 ;Global Smooth Solutions to the 2-D Inhomogeneous Navier-Stokes Equations with Variable Viscosity[J];Chinese Annals of Mathematics;2009年05期

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本文編號(hào)：2488323