论文标题
汉堡方程的分析性和较大的时间行为
Analyticity and large time behavior for the Burgers equation with the critical dissipation
论文作者
论文摘要
本文涉及汉堡方程的库奇问题，并涉及临界耗散。根据频率分解方法研究了空间和时间变量的适当性和分析性。对于任何大型初始数据，揭示了较大的时间行为。结果，可以表明，只要时间为正，并且像泊松内核一样，随着时间的变化趋于无限，任何平滑且可集成的解决方案都在空间和时间上进行分析。对于准地藻方程，相应的结果也被刺激。
This paper is concerned with the Cauchy problem of the Burgers equation with the critical dissipation. The well-posedness and analyticity in both of the space and the time variables are studied based on the frequency decomposition method. The large time behavior is revealed for any large initial data. As a result, it is shown that any smooth and integrable solution is analytic in space and time as long as time is positive and behaves like the Poisson kernel as time tends to infinity. The corresponding results are also obtined for the quasi-geostrophic equation.
