scholarly journals The Periodic Boundary Value Problem for the Weakly Dissipativeμ-Hunter-Saxton Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Zhengyong Ouyang ◽  
Xiangdong Wang ◽  
Haiwu Rong
Keyword(s):  
Boundary Value Problem ◽  
Besov Space ◽  
Periodic Boundary ◽  
Critical Case ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Well Posedness

We study the periodic boundary value problem for the weakly dissipativeμ-Hunter-Saxton equation. We establish the local well-posedness in Besov spaceB2,13/2, which extends the previous regularity range to the critical case.

scholarly journals The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Yun Wu ◽  
Zhengrong Liu ◽  
Xiang Zhang
Keyword(s):  
Evolution Equation ◽  
Boundary Value Problem ◽  
Besov Space ◽  
Besov Spaces ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Solution Map ◽  
Well Posed

This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type:∂tu+f(u)∂xu+F(u)=0,x∈T=R/2πZ,t∈R+. Under some conditions, we prove that this equation is locally well-posed in Besov spaceBp,rs(T). Furthermore, we study the continuity of the solution map for this equation inB2,rs(T). Our work improves some earlier results.

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