oseen方程弱解和强解的存在性

The Existence of Weak and Strong Solutions for Oseen Equations

我们讨论了Oseen方程当对流函数的散度不为零时弱解和强解的存在性.利用Lax-Milgram定理,证明了在空间H^1(Ω)中弱解的存在性.在此基础上,应用重复迭代及对偶原理等方法进一步证明了在一般的Sobolev空间中弱解和强解的存在性,并得到相应的解的不等式估计.

We deal with the existence of weak and strong solutions for Oseen equations in the case that the divergence of convective vector is nonzero. Using Lax Milgram Theorem, we first prove the existence of weak solution in H1 （Ω）, and then on the basis of this result, we use methods of iterative and dual principle to prove the existence of weak and strong solutions in generic Sobolev spaces and obtain corresponding estimates for these solutions.