Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation
Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation
<p style='text-indent:20px;'>We consider the low regularity behavior of the fourth order cubic nonlinear Schrödinger equation (4NLS) <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \begin{cases} i\partial_tu+\partial_x^4u = \pm \vert u \vert^2u, \quad(t,x)\in \mathbb{R}\times \mathbb{R}\\ u(x,0) = u_0(x)\in H^s\left(\mathbb{R}\right). \end{cases} \end{align*} $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>In [<xref ref-type="bibr" rid="b29">29</xref>], the author showed that …