Endpoint Sobolev Theory for the Muskat Equation
文献类型：期刊论文
| 作者 | Alazard, Thomas1; Quoc-Hung Nguyen2 |
| 刊名 | COMMUNICATIONS IN MATHEMATICAL PHYSICS
 |
| 出版日期 | 2022-11-12 |
| 页码 | 60 |
| ISSN号 | 0010-3616 |
| DOI | 10.1007/s00220-022-04514-7 |
| 英文摘要 | This paper is devoted to the study of solutions with critical regularity for the two-dimensional Muskat equation. We prove that the Cauchy problem is well-posed on the endpoint Sobolev space of L-2 functions with three-half derivative in L-2. This result is optimal with respect to the scaling of the equation. One well-known difficulty is that one cannot define a flow map such that the lifespan is bounded from below on bounded subsets of this critical Sobolev space. To overcome this, we estimate the solutions for a norm which depends on the initial data themselves, using the weighted fractional Laplacians introduced in our previous works. Our proof is the first in which a null-type structure is identified for the Muskat equation, allowing to compensate for the degeneracy of the parabolic behavior for large slopes. |
| 资助项目 | French National Research Agency (ANR)[ANR-18-CE40-0027] ; Academy ofMathematics and Systems Science, Chinese Academy of Sciences startup fund ; National Natural Science Foundation of China[12050410257] ; National Natural Science Foundation of China[12288201] ; National Key R&D Program of China[2021YFA1000800] |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000882353600003 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60613]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Alazard, Thomas |
| 作者单位 | 1.Univ Paris Saclay, Ctr Borelli UMR9010, ENS Paris Saclay, CNRS, Ave Sci, F-91190 Gif Sur Yvette, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Alazard, Thomas,Quoc-Hung Nguyen. Endpoint Sobolev Theory for the Muskat Equation[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2022:60. |
| APA | Alazard, Thomas,&Quoc-Hung Nguyen.(2022).Endpoint Sobolev Theory for the Muskat Equation.COMMUNICATIONS IN MATHEMATICAL PHYSICS,60. |
| MLA | Alazard, Thomas,et al."Endpoint Sobolev Theory for the Muskat Equation".COMMUNICATIONS IN MATHEMATICAL PHYSICS (2022):60. |
入库方式： OAI收割
来源：数学与系统科学研究院
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