Low Regularity Well-Posedness for the 3D Viscous Non-resistive MHD System with Internal Surface Wave

2020 ◽  
Vol 23 (1) ◽  
Author(s):  
Xiaoxia Ren ◽  
Zhaoyin Xiang
Keyword(s):  
Surface Wave ◽  
Internal Surface ◽  
Well Posedness ◽  
Low Regularity ◽  
Mhd System

Low regularity well-posedness for the viscous surface wave equation

2019 ◽  
Vol 62 (10) ◽  
pp. 1887-1924 ◽  
Author(s):  
Xiaoxia Ren ◽  
Zhaoyin Xiang ◽  
Zhifei Zhang
Keyword(s):  
Wave Equation ◽  
Surface Wave ◽  
Well Posedness ◽  
Low Regularity

scholarly journals LOW REGULARITY WELL-POSEDNESS OF THE DIRAC–KLEIN–GORDON EQUATIONS IN ONE SPACE DIMENSION

2008 ◽  
Vol 10 (02) ◽  
pp. 181-194 ◽  
Author(s):  
SIGMUND SELBERG ◽  
ACHENEF TESFAHUN
Keyword(s):  
Dirac Operator ◽  
Space Dimension ◽  
One Dimension ◽  
Well Posedness ◽  
Low Regularity ◽  
Klein Gordon ◽  
One Space Dimension

We extend recent results of Machihara and Pecher on low regularity well-posedness of the Dirac–Klein–Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections for the Dirac operator. We also show that the result is best possible up to endpoint cases, if one iterates in Bourgain–Klainerman–Machedon spaces.

scholarly journals Well posedness for the Kawahara equation on the half-line

2020 ◽  
Author(s):  
Boling Guo ◽  
fengxia liu
Keyword(s):  
Initial Data ◽  
Local Existence ◽  
Half Line ◽  
Well Posedness ◽  
Kawahara Equation ◽  
Low Regularity ◽  
Regularity Properties

We study the low-regularity properties of the Kawahara equation on the half line. We obtain the local existence, uniqueness, and continuity of the solution. Moreover, We obtain that the nonlinear terms of the solution are smoother than the initial data.

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