Self-similar solutions to the hypoviscous Burgers and SQG equations at criticality

被引：1
作者：
Ohkitani, Koji [1 ]
机构：
[1] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2023年 / 56卷 / 27期
关键词：
self-similarity; scale-invariance; hypoviscosity; Burgers equation; SQG equation; LARGE TIME BEHAVIOR; SINGULARITIES;
D O I：
10.1088/1751-8121/acdb12
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
After reviewing the source-type solution of the Burgers equation with standard dissipativity, we study the hypoviscous counterpart of the Burgers equation. (1) We determine an equation that governs the near-identity transformation underlying its self-similar solution. (2) We develop its approximation scheme and construct the first-order approximation. (3) We obtain the source-type solution numerically by the Newton-Raphson iteration scheme and find it to agree well with the first-order approximation. Implications of the source-type solution are given, regarding the possibility of linearisation of the hypoviscous Burgers equation. Finally we address the problems of the incompressible fluid equations in two dimensions, centering on the surface quasi-geostrophic equation with standard and hypoviscous dissipativity.
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页数：23
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