具有白噪声初始条件的二维Euler方程的弱涡量列式
Weak vorticity formulation of 2D Euler equations with white noise initial condition
摘要：
考虑了具有随机初始条件的二维欧拉方程组，初始条件按高斯测度分布。S. Albeverio和A.- B.克鲁塞罗是重新访问，弱涡制定的方法。一个解决方案被构造为一个限制的随机点涡。这就可以证明它也是L^ \infty -涡度解的极限。结果被推广到初始措施，有一个连续的有界密度相对于原来的高斯措施。
英文摘要：
The 2D Euler equations with random initial condition distributed as a certain Gaussian measure are considered. The theory developed by S. Albeverio and A.-B. Cruzeiro is revisited, following the approach of weak vorticity formulation. A solution is constructed as a limit of random point vortices. This allows to prove that it is also limit of L^\infty-vorticity solutions. The result is generalized to initial measures that have a continuous bounded density with respect to the original Gaussian measure.
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