Navier-Stokes方程解的Blow-up下界和Euler方程解的整体存在性
发布时间：2018-11-15 14:51
【摘要】：本论文分别对Euler方程解的整体存在性和Navier-Stokes方程解的爆破下界进行了研究,利用插入不等式,在齐次Sobolev空间H~s(s≥3/2)中,得到了Navier-Stokes方程解的爆破下界,推广了Younsi[26]工作的结果;对于三维带有科氏力的Navier-Stokes方程,我们将一般Navier-Stokes方程的结果推广到带有科氏力的Navier-Stokes方程中,利用Littlewood-Paley分解,得到了在齐次Sobolev空间H~s(s≥3/2)中解的爆破下界;我们还研究了Euler方程解的整体存在性和唯一性问题,通过研究Euler方程在弱型Besov空间的局部存在性和爆破结果,利用算子估计和嵌入性质,通过对解和压力项的范数进行先验估计,证明了当9)=2时,Euler方程在弱型Besov空间,(?),1p∞,sn/p+1,1≤r≤∞中解的整体存在性和唯一性。
[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，
本文编号：2333611
[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，
本文编号：2333611
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