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math.AP2025
Complex-valued solutions of the mKdV equations in generalized Fourier-Lebesgue spaces
Zijun Chen, Zihua Guo, Chunyan Huang
We study the \emph{complex-valued} solutions to the Cauchy problem of the modified Korteweg-de Vries equation on the real line. To study the low-regularity problems, we employ a ge…
math.AP2024
Local well-posedness for dispersion generalized Benjamin-Ono equations in Fourier-Lebesgue spaces
Zijun Chen
We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation where \begin{eqnarray*} \left\{ \begin{array}{l} \partial_t u+|\partial_x|^{1+α}…