带有分数阶耗散的三维广义Oldroyd-B模型的整体正则性

摘要/Abstract

摘要：

该文考虑了三维共旋情形下，带有分数阶耗散（-△）^η₁u和（-△）^η₂τ的广义不可压缩Oldroyd-B模型.假设初始数据（u₀，τ₀）充分光滑，若耗散指标η₁ ≥ 5/4，η₂ ≥ 5/4，利用能量方法，得到了方程组经典解的整体正则性.

关键词: Oldroyd-B模型, 分数阶Laplace耗散, 整体正则性

Abstract:

In this paper, we consider the 3D generalized Oldroyd-B type models with fractional Laplacian dissipation (-△)^η₁u and (-△)^η₂τ in the corotational case. By using energy method, for η₁ ≥ 5/4 and η₂ ≥ 5/4, we obtain the global regularity of classical solutions when the initial data (u₀, τ₀) are sufficiently smooth.

Key words: Oldroyd-B type models, Fractional Laplacian dissipation, Global regularity

中图分类号:

O175.29

张秋月. 带有分数阶耗散的三维广义Oldroyd-B模型的整体正则性[J]. 数学物理学报, 2019, 39(5): 1125-1135.

Qiuyue Zhang. Global Regularity for 3D Generalized Oldroyd-B Type Models with Fractional Dissipation[J]. Acta mathematica scientia,Series A, 2019, 39(5): 1125-1135.

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