Bibliographic Details
| Title: |
Nonexistence of Minimal Mass Blow-Up Solution for the 2D Cubic Zakharov–Kuznetsov Equation. |
| Authors: |
Chen, Gong1 (AUTHOR) gc@math.gatech.edu, Lan, Yang2 (AUTHOR) lanyang@mail.tsinghua.edu.cn, Yuan, Xu3 (AUTHOR) xu.yuan@amss.ac.cn |
| Source: |
SIAM Journal on Mathematical Analysis. 2025, Vol. 57 Issue 6, p5950-5975. 26p. |
| Subjects: |
Modulation theory, Lyapunov functions, Partial differential equations, Ordinary differential equations, Function spaces, Mass (Physics) |
| Abstract: |
For the 2D cubic (mass-critical) Zakharov–Kuznetsov equation, \(\partial_t\phi +\partial_{x_1} (\Delta \phi +\phi^3)=0\) , \((t,x)\in [0,\infty)\times \mathbb{R}^{2}\) , we prove that there exist no finite/infinite time blow-up solution with minimal mass in the energy space. This nonexistence result is in contrast to the one obtained by Martel–Merle–Raphaël [J. Eur. Math. Soc. (JEMS), 17 (2015), pp. 1855–1925] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. The proof relies on a refined ODE argument related to the modulation theory and a modified energy-virial Lyapunov functional with a monotonicity property. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
