四维定常 Navier-Stokes 方程离散自相似解的存在性——献给陈化教授 70 寿辰

Abstract

Abstract:

In this paper, we prove that there exists at least one discretely self-similar solution to the steady Navier-Stokes equations in $\mathbb{R}^4\backslash\{0\}$ for any given locally Lipschitz discretely self-similar external force. If the external force is smooth away from the origin, the constructed discretely self-similar solution is also smooth away from the origin. Notably, the existence result does not require any smallness assumption on the external force.

Key words: steady Navier-Stokes equations, discretely self-similar solutions, four dimension, existence

CLC Number:

O175.29

Hao Liu, Yun Wang, Chunjing Xie. Existence of Discretely Self-Similar Solutions to Four-Dimensional Steady Navier-Stokes Equations[J].Acta mathematica scientia,Series A, 2026, 46(2): 709-723.

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Existence of Discretely Self-Similar Solutions to Four-Dimensional Steady Navier-Stokes Equations

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