[1] Zhu Min,. Notes on well-posedness for the b-family equation [J]. Journal of Southeast University (English Edition), 2014, 30 (1): 128-134. [doi:10.3969/j.issn.1003-7985.2014.01.024]

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Notes on well-posedness for the b-family equation

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

30

Issue:

2014 1

Page:

128-134

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2014-03-31

Info

Title:

Notes on well-posedness for the b-family equation

Author(s):

Zhu Min

Department of Mathematics, Southeast University, Nanjing 211189, China
Department of Mathematics, Nanjing Forestry University, Nanjing 210036, China

Keywords:

b-family equation;  Besov space;  local well-posedness

PACS:

O175

DOI:

10.3969/j.issn.1003-7985.2014.01.024

Abstract:

The local well-posedness for the b-family equation in the critical space is studied. Applying the Littlewood-Paley decomposition method in the critical Besov spaces B^ss_{2, r} with the index s=3/2, which is the generalization space of the Sobolev spaces H ^ss, it is established that there is a maximal time T=T(u₀)>0 such that for the b-family equation there exists a unique solution u(t, x)∈C(［0, T］;B^3/2_{2, 1})∩C¹(［0, T］;B¹_{2, 1})when the initial variable u₀(x)∈B^3/2_{2, 1} is the critical regularity. Moreover, the solution u(x, t)depends continuously on the initial data u₀(x). Furthermore, using the abstract Cauchy-Kowalevski theorem to prove the analytic regularity of the solutions for the b-family equation in a suitable scale of Banach spaces E, it is shown that the solutions of the b-family are analytic in both variables, globally in space and locally in time, when the initial data is analytic.

References:

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Memo

Memo:

Biography: Zhu Min(1981—), female, doctor, zhumin@njfu.edu.cn.
Foundation item: The Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.13KJB110012).
Citation: Zhu Min. Notes on well-posedness for the b-family equation[J].Journal of Southeast University(English Edition), 2014, 30(1):128-134.[doi:10.3969/j.issn.1003-7985.2014.01.024]

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