Global existence and lifespan for semilinear wave equations with mixed nonlinear terms
| Autor: | Dai, Wei, Fang, Daoyuan, Wang, Chengbo |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jde.2019.04.007 |
| Popis: | Firstly, we study the equation $\square u = |u|^{q_c}+ |\partial u|^p$ with small data, where $q_c$ is the critical power of Strauss conjecture and $p\geq q_c.$ We obtain the optimal lifespan $\ln({T_\varepsilon})\approx\varepsilon^{-q_c(q_c-1)}$ in $n=3$, and improve the lower-bound of $T_\varepsilon$ from $\exp({c\varepsilon^{-(q_c-1)}})$ to $\exp({c\varepsilon^{-(q_c-1)^2/2}})$ in $n=2$. Then, we study the Cauchy problem with small initial data for a system of semilinear wave equations $\square u = |v|^q,$ $ \square v = |\partial_t u|^p$ in 3-dimensional space with $q<2$. We obtain that this system admits a global solution above a $p-q$ curve for spherically symmetric data. On the contrary, we get a new region where the solution will blow up. Comment: Final version, to appear in Journal of Differential Equations. 22 pages, 1 figure |
| Databáze: | arXiv |
| Externí odkaz: |
|