关于四元数Burgers方程的奇异性

IF 0.5 Q3 MATHEMATICS Annales Mathematiques du Quebec Pub Date : 2021-10-20 DOI:10.1007/s40316-021-00175-5

Vladimir Sverak

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引用次数: 1

摘要

我们考虑了\（q:｛\mathbf｛R｝｝}\times（0，\infty）\rightarrow｛\math bf{H｝}\）（四元数）的方程\（q_t+qq_x=q_｛xx｝\），并表明虽然奇点可以从光滑紧支持的数据中发展，但这种情况是非一般的。在初始数据的任意小的“一般”平滑扰动下，奇点将消失。对于\（\mathbf｛S｝^1 \times（0，\infty）\）中的同一方程，也建立了类似的结果，其中\（\math bf｝^1）是标准的一维圆。

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On singularities in the quaternionic Burgers equation

We consider the equation \(q_t+qq_x=q_{xx}\) for \(q:{{\mathbf {R}}}\times (0,\infty )\rightarrow {\mathbf {H}}\) (the quaternions), and show that while singularities can develop from smooth compactly supported data, such situations are non-generic. The singularities will disappear under an arbitrary small “generic” smooth perturbation of the initial data. Similar results are also established for the same equation in \(\mathbf{S}^1\times (0,\infty )\), where \(\mathbf{S}^1\) is the standard one-dimensional circle.

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Annales Mathematiques du Quebec MATHEMATICS-

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1.10

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期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.

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