Well-posedness of a 1D transport equation with nonlocal velocity in the Lei-Lin space

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• 作者：Yanghai Yu ; Xing Wu and Yanbin Tang
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：40
• 期：4
• 页码：947-956
• 全文大小：190K
• ISSN：1099-1476

文摘

In this paper, we consider the well-posedness of a one-dimensional transport equation with nonlocal velocity in the Lei–Lin space www.w3.org/1998/Math/MathML">w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">w>Xw>w>sw>w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">(w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML" mathvariant="double-struck">Rw="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">). We first modify the product estimate and then establish the global existence of solutions to the Cauchy problem with small enough initial data. Finally, we discuss the stability of the global solution. Copyright