Lifeng Zhao

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math.AP2026

Nonexistence of blow-up solutions with smooth radiation for energy-critical equivariant wave maps

Jacek Jendrej, Yuchen Yin, Lifeng Zhao

We study $k$ -equivariant energy critical wave maps $R^{1 + 2} \to S^{2}$ , for any equivariance degree $k \geq 2$ . We prove that the radiation associated with any finite…

math.AP2026

Soliton resolution for the energy critical damped wave equations in the radial case

Jingyuan Gu, Lifeng Zhao

We consider energy-critical damped wave equation \begin{equation*} \partial_{tt}u-Îu+Î±\partial_t u=\left|u\right|^{\frac{4}{D-2}}u \end{equation*} with radial initial data in dim…

math.AP2026

Construction of multi-bubble solutions for the energy-critical wave equation in dimension four

Jingyuan Gu, Jacek Jendrej, Lifeng Zhao

For any $N \geq 2$ , we construct a global solution of the energy-critical focusing wave equation in dimension four which blows up in infinite time at $N$ prescribed points $z_1,\ldo…

math.AP2026

Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five

Jacek Jendrej, Chencheng Zhang, Lifeng Zhao

We study the asymptotic dynamics of multi-bubble solutions to the focusing energy-critical wave equation in five dimensions. Assuming that the solution asymptotically decomposes in…

math.AP2024

Dynamics for the corotational energy-critical wave map equation with quantized blow-up rates

Ze Li, Yezhou Yi, Lifeng Zhao

We consider the wave maps from $R^{1 + 2}$ into $S^{2} \subset R^{3} .$ Under an additional assumption of $k$ -corotational symmetry, the problem reduces to the o…