On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data
نویسندگان
چکیده
We prove that the Cauchy problem for Muskat equation is well-posed locally in time any initial data critical space of Lipschitz functions with three-half derivative $$L^2$$ . Moreover, we solution exists globally under a smallness assumption.
منابع مشابه
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برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولWell-posedness of the Muskat problem with H2 initial data
Article history: Received 30 December 2014 Accepted 13 August 2015 Available online xxxx Communicated by Charles Fefferman MSC: 35R35 35Q35 35S10 76B03
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ژورنال
عنوان ژورنال: Annals of PDE
سال: 2021
ISSN: ['2524-5317', '2199-2576']
DOI: https://doi.org/10.1007/s40818-021-00099-x