一般非线性演化方程的“暴力进程”及有关问题的讨论

The “Rebel Travelling” of General Nonlinear Evolutional Equation and Discussion on Related Problems

本文为系列讨论非线性演化方程“自身摧毁效应”的工作之一·文献［１，２］已讨论了流体力学的Ｎａｖｉｅｒ＿Ｓｔｏｃｋｅｓ方程非线性演化的溃变·本文又进行了某些扩展，并涉及一、二阶模型的溃变和高阶复合型的“暴力进程”·结果表明，某些模型可在一定条件出现“半破裂”；溃变体现在整体演化中；对流体而言，弱非线性模型的人为性较强，且基于连续性思维的数值积分的平滑格式，及类似的作法或提法有待商榷·

This paper is a part of series works for discussing the “auto_destruction effects” of general nonlinear evolutional equations.The blown_up of Navier_Stockes equation is discussed in references .Some expansion is made in this paper,and the blown_up of order 1 or 2 models and the “rebel travelling” of complex model of poly_order are discussed.The results indicate that “semi_rupture” appears for some models on specific condition;the blown_up appears during the whole evolution.For fluid,however,the weakly_nonlinear model is of more artiliciality and there is much room for arguing about the smoothing scheme of the numerical integral on the basis of continuous thinking and so on.