scholarly journals Local Well-Posedness of Prandtl Equations for Compressible Flow in Two Space Variables

2015 ◽  
Vol 47 (1) ◽  
pp. 321-346 ◽  
Author(s):  
Ya-Guang Wang ◽  
Feng Xie ◽  
Tong Yang
Keyword(s):  
Compressible Flow ◽  
Well Posedness ◽  
Prandtl Equations

Well-posedness of Prandtl equations with non-compatible data

Nonlinearity ◽  
2013 ◽  
Vol 26 (12) ◽  
pp. 3077-3100 ◽  
Author(s):  
M Cannone ◽  
M C Lombardo ◽  
M Sammartino
Keyword(s):  
Well Posedness ◽  
Prandtl Equations

scholarly journals On well-posedness of Ericksen–Leslie’s parabolic–hyperbolic liquid crystal model in compressible flow

2019 ◽  
Vol 29 (01) ◽  
pp. 121-183
Author(s):  
Ning Jiang ◽  
Yi-Long Luo ◽  
Shaojun Tang
Keyword(s):  
Liquid Crystal ◽  
Compressible Flow ◽  
Stokes Equations ◽  
Initial Energy ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Crystal Model ◽  
Energy Law ◽  
Time Existence

We study the well-posedness of the Ericksen–Leslie’s parabolic–hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case [N. Jiang and Y.-L. Luo, On well-posedness of Ericsen–Leslie’s hyperbolic incompressible liquid crystal model, preprint (2017), arXiv:1709.06370v1 ] and some techniques from compressible Navier–Stokes equations, we first prove the local-in-time existence of the classical solution to the system with finite initial energy, under some natural constraints on the Leslie coefficients which ensure that the basic energy law is dissipative. Furthermore, with an additional assumption on the coefficients which provides a damping effect, and the smallness of the initial energy, the existence of global solution can be established.

scholarly journals A well-posedness theory for the Prandtl equations in three space variables

2017 ◽  
Vol 308 ◽  
pp. 1074-1126 ◽  
Author(s):  
Cheng-Jie Liu ◽  
Ya-Guang Wang ◽  
Tong Yang
Keyword(s):  
Well Posedness ◽  
Prandtl Equations ◽  
Three Space

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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