摘要
We study the global well-posedness of large-data solutions to the Cauchy problem of the energy critical Cahn-Hilliard-Brinkman equations in R^(4).By developing delicate energy estimates,we show that for any given initial datum in H^(5)(R^(4)),there exists a unique global-in-time classical solution to the Cauchy problem.As a special consequence of the result,the global well-posedness of large-data solutions to the energy critical Cahn-Hilliard equation in R^(4) follows,which has not been established since the model was first developed over 60 years ago.The proof is constructed based on extensive applications of Gagliardo-Nirenberg type interpolation inequalities,which provides a unified approach for establishing the global well-posedness of large-data solutions to the energy critical Cahn-Hilliard and Cahn-Hilliard-Brinkman equations for spatial dimension up to four.
基金
Support for this work came in part from a National Natural Science Foundation of China Award 12001064(F.Wang)
a Hunan Education Department Project 20B006(F.Wang)
a Double First-Class International Cooperation Expansion Project 2019IC39(F.Wang)
a National Natural Science Foundation of China Award 12171116(L.Xue)
a Fundamental Research Funds for Central Universities of China Award 3FT2020CFT2402(L.Xue)
a Natural Science Foundation of Jiangsu Province of China Award BK20200346(K.Yang)
from Simons Foundation Collaboration Grant for Mathematicians Award 413028(K.Zhao)
funding from the Shuang Chuang Doctoral Plan of Jiangsu Province of China.
