Solvability of the First Initial-boundary Value Problem for the Quasihydrodynamics Equations in the Shallow Water Approximation

被引：0
作者：
Evseev, F. A. [1 ,2 ]
Pyatkov, S. G. [1 ,3 ]
机构：
[1] Yugra State Univ, Khanty Mansiysk 628012, Russia
[2] Shpilman Res & Analyt Ctr Rat Use Subsoil, Khanty Mansiysk 628007, Russia
[3] Acad Sci Republ Sakha Yakutia, Yakutsk, Russia
来源：
LOBACHEVSKII JOURNAL OF MATHEMATICS | 2024年 / 45卷 / 09期
关键词：
initial-boundary value problem; quasi-hydrodynamic system; a priori estimate; regular solution; shallow water approximation; CLASSICAL-SOLUTIONS; EXISTENCE;
D O I：
10.1134/S1995080224605083
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The unique solvability of an analog of the first initial boundary value problem for the quasihydrodynamics equations in the shallow water approximation is established under certain conditions on the data. A solution is regular , i.e., all generalized derivatives occurring in the equation are summable to some power. The proof relies on a priori estimates and the contraction mapping principle.
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页码：4490 / 4499
页数：10
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