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On the Growth in Time of Sobolev Norms for TimeDependent Linear Generalized KdV-typeEquations
  
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KeyWord:Sobolev norms; Time dependent linear generalized KdV-type equa- tion; Fixed analytic potential
Author NameAffiliation
Chengming Cao School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
Xiaoping Yuan School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
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Abstract:
      We give a detailed description in 1-D the growth of Sobolev norms for time dependent linear generalized KdV-type equations on the circle. For most initial data, the growth of Sobolev norms is polynomial in time for fixed analytic potential with admissible growth. If the initial data are given in a fixed smaller function space with more strict admissible growth conditions for V (x,t) , then the growth of previous Sobolev norms is at most logarithmic in time.