三维可压缩欧拉方程弱解的寿命界与超经典传播
Lifespan Bounds and Super-Classical Propagation for Weak Solutions of the Three-Dimensional Compressible Euler Equations
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中文总结 AI 辅助
研究三维可压缩欧拉方程有界弱解寿命界，在特定条件下建立上界，指出超此上界的解会以超经典速度传播且伴有跳跃间断。
中文摘要 AI 辅助
我们在初始数据的局部正性条件以及扰动的本质支撑传播到未扰动背景状态的速度不超过经典局部适定性预测速度的假设下，建立了三维等熵可压缩欧拉方程在\([0,T)\times\mathbb R^3\)上有界弱解寿命的上界。进一步表明，任何具有有界逆密度且持续超过此上界的熵容许有界弱解，必定以严格超经典速度传播到未扰动区域，且这种加速传播必然伴随着解的相关单侧\(L^\infty\)轮廓中的跳跃间断。
英文摘要
We establish an upper bound on the lifespan of bounded weak solutions to the three-dimensional isentropic compressible Euler equations on $[0,T)\times\mathbb R^3$, under a localized positivity condition on the initial data and the assumption that the essential support of the disturbance propagates into an undisturbed background state no faster than predicted by classical local well-posedness. We further show that any entropy-admissible bounded weak solution with bounded inverse density that persists beyond this upper bound must propagate into the undisturbed region at a strictly super-classical speed and that this accelerated propagation is necessarily accompanied by a jump discontinuity in an associated one-sided $L^\infty$-profile of the solution.
