Convergence of approximating solutions of the Navier–Stokes equations in higher ordered Sobolev norms

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-04-14 DOI:10.1002/mana.12009

Yuta Koizumi

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引用次数: 0

Abstract

We show that the approximating solutions ${u_{j}}_{j = 0}^{\infty}$ of the Navier–Stokes equations constructed by Kato with the initial data $u (0) \in L_{σ}^{n} (R^{n})$ converge to the local strong solution $u$ in the topology of $W^{k, q} (R^{n})$ for all $k \in N$ provided the convergence in the scaling invariant norm in $L^{q} (R^{n})$ with the time weight holds. As an application of our convergence, it is clarified that the approximation of the pressure is established in $W^{k + 1, q} (R^{n})$ .

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高阶Sobolev范数下Navier-Stokes方程近似解的收敛性

我们证明了Kato用初始数据构造的Navier-Stokes方程的近似解{u j} j = 0∞$\lbrace u_j\rbrace _{j=0}^{\infty }$u(0)∈L σ n (rn) $u(0) \in L_{\sigma }^{n}(\mathbb {R}^{n})$收敛到W k拓扑中的局部强解u $u$，q (R n) $W^{k,q}(\mathbb {R}^n)$对于所有k∈n $k \in \mathbb {N}$提供了尺度不变范数的收敛性在lq (R n) $L^q(\mathbb {R}^n)$中，时间权值保持不变。作为我们收敛性的一个应用，可以清楚地看出压力的近似是在W k + 1中建立的，q (rn) $W^{k+1,q}(\mathbb {R}^n)$。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index