Global well-posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

2018 ◽  
Vol 42 (3) ◽  
pp. 747-766
Author(s):  
Zhilin Lin ◽  
Bingyuan Huang ◽  
Jinrui Huang
Keyword(s):  
Classical Solutions ◽  
Well Posedness ◽  
Magnetohydrodynamic Equations ◽  
Potential Force ◽  
Large Potential

On the classical solutions for a Rosenau–Korteweg-deVries–Kawahara type equation

2021 ◽  
pp. 1-23
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Cauchy Problem ◽  
Small Amplitude ◽  
Type Equation ◽  
Discrete Systems ◽  
Finite Depth ◽  
Capillary Waves ◽  
Classical Solutions ◽  
Well Posedness ◽  
Kawahara Equation ◽  
The Cauchy Problem

The Rosenau–Korteweg-deVries–Kawahara equation describes the dynamics of dense discrete systems or small-amplitude gravity capillary waves on water of a finite depth. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem.

scholarly journals A moving boundary problem for the Stokes equations involving osmosis: Variational modelling and short-time well-posedness

2015 ◽  
Vol 27 (4) ◽  
pp. 647-666
Author(s):  
FRIEDRICH LIPPOTH ◽  
MARK A. PELETIER ◽  
GEORG PROKERT
Keyword(s):  
Surface Tension ◽  
Boundary Problem ◽  
Osmotic Pressure ◽  
Moving Boundary ◽  
Stokes Equations ◽  
Semipermeable Membrane ◽  
Moving Boundary Problem ◽  
Classical Solutions ◽  
Well Posedness ◽  
Short Time

Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For this problem we prove the existence of classical solutions for a short-time.

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