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math.AP2023★ 1 cited
Energy solutions for the fifth-order modified Korteweg de-Vries equations
Chulkwang Kwak, Kiyeon Lee
We consider the Cauchy problem for the fifth-order modified Korteweg-de Vries equation (mKdV) under the periodic boundary condition. The fifth-order mKdV is an asymptotic model for…
math.AP2021
Ill-posedness issues on -Boussinesq system
Chulkwang Kwak, Christopher Maulén
In this paper, we consider the Cauchy problem for -Boussinesq system posed on one- and two-dimensional Euclidean spaces. This model, initially introduced by Bona, Chen, and…
math.AP2012★ 1 cited
Rough solutions of the fifth-order KdV equations
Zihua Guo, Chulkwang Kwak, Soonsik Kwon
We consider the Cauchy problem of the fifth-order equation arising from the Korteweg-de Vries (KdV) hierarchy u_t + u_{xxxxx} + c_1u_{x} u_{xx} + c_2u u_{x} = 0 x,t \in \R We prove…