广义无粘曲面拟地转方程不爆破的若干条件

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Mathematical Physics Pub Date : 2023-10-30 DOI:10.1155/2023/4420217
Linrui Li, Mingli Hong, Lin Zheng
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引用次数: 0

摘要

在本文中,我们研究了以下广义修正无粘曲面拟地转方程(GSQG) θ t + u·∇θ = 0, u =∇⊥ψ, - Λ β ψ = θ, θ x, 0 = θ 0 x的一些非爆破结果。这是一个广义曲面拟等转方程(GSQG),其速度场u与标量θ的关系为u = -∇⊥Λ - β θ,其中1≤β≤2。证明了广义拟等转方程的水平集不存在双曲鞍时不存在有限时间奇点,且鞍的开口角最多以指数衰减的形式趋近于零。此外,我们还给出了广义无粘面拟等转方程不形成尖锐锋的一些条件,并得到了半均匀锋形成的一些估计。这些结果大大削弱了排除简单双曲鞍在有限时间内坍缩的几何假设。
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Some Conditions of Non-Blow-Up of Generalized Inviscid Surface Quasigeostrophic Equation
In this paper, we survey some non-blow-up results for the following generalized modified inviscid surface quasigeostrophic equation (GSQG) θ t + u · θ = 0 , u = ψ , Λ β ψ = θ , θ x , 0 = θ 0 x . . This is a generalized surface quasigeostrophic equation (GSQG) with the velocity field u related to the scalar θ by u = Λ β θ , where 1 β 2 . We prove that there is no finite-time singularity if the level set of generalized quasigeostrophic equation does not have a hyperbolic saddle, and the angle of opening of the saddle can go to zero at most as an exponential decay. Moreover, we give some conditions that rule out the formation of sharp fronts for generalized inviscid surface quasigeostrophic equation, and we obtain some estimates on the formation of semiuniform fronts. These results greatly weaken the geometrical assumptions which rule out the collapse of a simple hyperbolic saddle in finite time.
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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