Constantin P, Nie Q, Schörghofer N
Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Sep;60(3):2858-63. doi: 10.1103/physreve.60.2858.
We study the formation of thermal fronts in an active scalar equation that is similar to the Euler equation. For a particular initial condition, an earlier candidate for finite-time blowup, the front forms in a generalized self-similar way with constant hyperbolicity at the center. The behavior belongs to a class of scenarios for which finite-time blowup is impossible. A systematic exploration of many different initial conditions reveals no evidence of singular solutions.
我们研究了一个类似于欧拉方程的有源标量方程中热锋的形成。对于一个特定的初始条件，即一个较早的有限时间爆破候选条件，锋以广义自相似的方式形成，中心具有恒定的双曲性。这种行为属于一类不可能出现有限时间爆破的情形。对许多不同初始条件的系统探索没有发现奇异解的证据。
