Korteweg型可压缩流体模型在临界情况下的全局适定性

IF 1.8 4区 数学 Q1 MATHEMATICS
Takayuki Kobayashi, M. Murata
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引用次数: 4

摘要

在本文中,我们考虑了Korteweg型可压缩流体模型,在给定的恒定状态下,压力导数等于$0$的临界情况下。结果表明,对于极大$L_p$-L_q$正则性类中的小初始数据,该系统允许一个唯一的全局强解。因此,我们还证明了非线性问题解的衰变估计。为了获得临界情况的全局适定性,我们在低频的附加假设下,给出了线性化方程解的$L_p$-L_q$衰变性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The global well-posedness of the compressible fluid model of Korteweg type for the critical case
In this paper, we consider the compressible fluid model of Korteweg type in a critical case where the derivative of pressure equals to $0$ at the given constant state. It is shown that the system admits a unique, global strong solution for small initial data in the maximal $L_p$-$L_q$ regularity class. As a result, we also prove the decay estimates of the solutions to the nonliner problem. In order to obtain the global well-posedness for the critical case, we show $L_p$-$L_q$ decay properties of solutions to the linearized equations under an additional assumption for a low frequencies.
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来源期刊
Differential and Integral Equations
Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.40
自引率
0.00%
发文量
0
审稿时长
6-12 weeks
期刊介绍: Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.
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