具有涡度的量子欧拉系统在维度 $d=2$ 中的全局弱轴对称解的稳定性

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED Acta Applicandae Mathematicae Pub Date : 2024-07-22 DOI:10.1007/s10440-024-00663-0

Boris Haspot, Marc-Antoine Vassenet

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引用次数: 0

摘要

我们考虑了量子欧拉系统在二维空间的全局弱解的稳定性。更确切地说，我们建立了全局有限能量弱解的紧凑性，只要这些初始数据是轴对称的。我们的主要论证基于马德隆变换，它使我们能够证明速度非旋转部分的新加藤估计。

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Stability of the Global Weak Axisymmetric Solution to the Quantum Euler System with Vorticity in Dimension $d=2$

We consider the stability of the global weak solution of the Quantum Euler system in two space dimensions. More precisely, we establish compactness properties of global finite energy weak solution for large initial data provided that these are axisymmetric. The main novelty is that the initial velocity is not necessary irrotational when the density is not vanishing, our main argument is based on the Madelung transform which enables us to prove new Kato estimates on the irrotational part of the velocity.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.