【摘要】：本論文分別對(duì)Euler方程解的整體存在性和Navier-Stokes方程解的爆破下界進(jìn)行了研究,利用插入不等式,在齊次Sobolev空間H~s(s≥3/2)中,得到了Navier-Stokes方程解的爆破下界,推廣了Younsi[26]工作的結(jié)果;對(duì)于三維帶有科氏力的Navier-Stokes方程,我們將一般Navier-Stokes方程的結(jié)果推廣到帶有科氏力的Navier-Stokes方程中,利用Littlewood-Paley分解,得到了在齊次Sobolev空間H~s(s≥3/2)中解的爆破下界;我們還研究了Euler方程解的整體存在性和唯一性問(wèn)題,通過(guò)研究Euler方程在弱型Besov空間的局部存在性和爆破結(jié)果,利用算子估計(jì)和嵌入性質(zhì),通過(guò)對(duì)解和壓力項(xiàng)的范數(shù)進(jìn)行先驗(yàn)估計(jì),證明了當(dāng)9)=2時(shí),Euler方程在弱型Besov空間,(?),1p∞,sn/p+1,1≤r≤∞中解的整體存在性和唯一性。
[Abstract]:In this paper, the global existence of the solution of Euler equation and the blow-up lower bound of the solution of Navier-Stokes equation are studied respectively. By using the insertion inequality, the lower bound of the solution of the Navier-Stokes equation is obtained in the homogeneous Sobolev space H _ s (s 鈮，

本文編號(hào)：2333611