Well-Posedness of the Dean–Kawasaki and the Nonlinear Dawson–Watanabe Equation with Correlated Noise

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-03-11 DOI:10.1007/s00205-024-01963-3

引用次数: 0

Abstract

In this paper we prove the well-posedness of the generalized Dean–Kawasaki equation driven by noise that is white in time and colored in space. The results treat diffusion coefficients that are only locally \({1}/{2}\) -Hölder continuous, including the square root. This solves several open problems, including the well-posedness of the Dean–Kawasaki equation and the nonlinear Dawson–Watanabe equation with correlated noise.

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具有相关噪声的迪安-川崎方程和非线性道森-瓦塔那贝方程的良好拟合度

摘要本文证明了广义迪安-川崎方程在时间上为白噪声、空间上为彩色噪声驱动下的良好求解性。结果处理了仅局部 \({1}/{2}\) -Hölder 连续的扩散系数，包括平方根。这解决了几个悬而未决的问题，包括 Dean-Kawasaki 方程和具有相关噪声的非线性 Dawson-Watanabe 方程的良好拟合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.