This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries (KdV) system in $\mathbb{R}^n$. We first prove, by the Leray-Schauder principle and the vanishing viscosity method, that any initial data $N$-dimensional vector value function $u_0(x)$ in Sobolev space $H^{s}(\mathbb{R}^n)$ $(s\geq1)$ leads to a global weak solution. Second, we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in $\mathbb{R}^2$ and $\mathbb{R}^3$.
Boling Guo
,
Yamin Xiao
. THE EXISTENCE OF WEAK SOLUTIONS AND PROPAGATION REGULARITY FOR A GENERALIZED KDV SYSTEM*[J]. Acta mathematica scientia, Series B, 2023
, 43(2)
: 942
-958
.
DOI: 10.1007/s10473-023-0225-1
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