关于无界域中 div-curl 问题的唯一可解性和解的能量估计

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI:10.1134/S0040577924110023

A. V. Gorshkov

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引用次数: 0

摘要

我们研究了在外部二维域边界上以无滑动条件从涡旋函数重建螺线矢量场的问题。作为涡旋函数与谐函数正交的条件，我们得到了一个可解性准则。我们还得到了在\(L_2\) 和\(H_1\) 空间中的解的一些估计值。

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On the unique solvability of the div–curl problem in unbounded domains and energy estimates of solutions

We study the problem of reconstructing a solenoidal vector field from a vortex function with a no-slip condition on the boundary of an external two-dimensional domain. A solvability criterion is obtained as a condition for the orthogonality of the vortex function to harmonic functions. We also obtain some estimates of the solution in the spaces \(L_2\) and \(H_1\).

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.