In this article, by following the strategies in dealing with supercritical cubic and quintic wave equations in (J. Eur. Math. Soc. (JEMS) 16 (2014) 1-30) and (J. Math. Pures Appl. ( 9) 105 (2016) 342-366), we obtain that, the equationThe key point here is that p−3 p−1 is much smaller than the critical index 3 2 − 2 p−1 for 3 < p < 5.
In this article, we prove that the equationThis work also indicates that, only properly regularizing the initial data can we smoothly approximate the solutions constructed in [2] and [12].
In this article, we follow the strategies, listed in [7] and [14], in dealing with supercritical cubic and quintic wave equations, we obtain that, the equationis almost surely global well-posed in the sense of Burq and Tzvetkov[7] for any s ∈ ( p−3 p−1 , 1). The key point here is that p−3 p−1 is much smaller than the critical index 3 2 − 2 p−1 for 3 < p < 5.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.