Global existence of solutions for the Cauchy problem of the Kawahara equation with \(L^2\) initial data (Q2505394)

The authors deal with the existence of a solution for the initial value problem \[ \partial_t u+\alpha u\,\partial_x u+\beta\partial^3_x u+\gamma\partial^5_x u= 0\quad\text{in }\mathbb R^2, \] \[ u(x,0)= u_0(x)\quad\text{for }x\in\mathbb R, \] where \(\alpha\), \(\beta\), \(\gamma\) are real constants \((\alpha,\gamma\neq 0)\), and \(u_0\) is a given functions.