Open AccessThe Muskat problem with 𝐶¹ data
Author(s) -
Ke Chen,
QuocHung Nguyen,
Yiran Xu
Publication year - 2022
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/8559
Subject(s) - algorithm , artificial intelligence , computer science
In this paper we prove that the Cauchy problem of the Muskat equation is wellposed locally in time for any initial data in C ˙ 1 ( R d ) ∩ L 2 ( R d ) \dot C^1(\mathbb {R}^d)\cap L^2(\mathbb {R}^d) .