4 papers
The Cauchy problem for higher-order modified Camassa-Holm equations on the circle
Wei Yan, Yongsheng Li, Xiaoping Zhai +1
In this paper, we investigate the Cauchy problem for the shallow water type equation \begin{eqnarray*} u_{t}+\partial_{x}^{2j+1}u + \frac{1}{2}\partial_{x}(u^{2})+ \partial_{x}(1-\…
The Cauchy problem for the shallow water typ equations in low regularity spaces on the circle
Wei Yan, Yongsheng LI, Xiaoping Zhai +1
In this paper, we investigate the Cauchy problem for the shallow water type equation \[ u_{t}+\partial_{x}^{3}u + \frac{1}{2}\partial_{x}(u^{2})+\partial_{x} (1-\partial_{x}^{2})^{…
The Cauchy problem for a higher order shallow water type equation on the circle
Wei Yan, Yongsheng Li, Jianhua Huang
In this paper, we investigate the Cauchy problem for a higher order shallow water type equation \begin{eqnarray*} u_{t}-u_{txx}+\partial_{x}^{2j+1}u-\partial_{x}^{2j+3}u+3uu_{x}-2u…
Global well-posedness for the 3-D density-dependent liquid crystal flows in the critical Besov spaces
Xiaoping Zhai, Yongsheng Li, Wei Yan
In this paper, we prove the local well-posedness of 3-D density-dependent liquid crystal flows with initial data in the critical Besov spaces, without assumptions of small density…