去奇异化狄拉克δ分布背景电荷下Vlasov-Poisson方程的梯度增长
Gradient Growth for Vlasov-Poisson in background charge distributed by Desingularized Dirac Delta
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中文总结 AI 辅助
本文通过构造具有局部双曲流的稳态解并利用特征速度场的$L^\infty$稳定性，证明了环面上一维Vlasov-Poisson方程的超线性梯度增长，方法受Denisov启发。
中文摘要 AI 辅助
我们证明了环面上的一维Vlasov-Poisson方程的超线性梯度增长。我们首先构造具有（局部）双曲流的稳态解来证明这一点。然后我们扰动该解，并利用特征速度场的$L^\infty$稳定性来证明超线性增长。该证明受Denisov工作的启发。
英文摘要
We prove the superlinear gradient growth for the one dimensional Vlasov-Poisson equation on the torus. We show them by first constructing the stationary solution which has a hyperbolic flow (locally). Then we perturb the solution and use the $L^\infty$ stability of the characteristic velocity field to show the superlinear growth. This proof was inspired by the work of Denisov.
