On the cauchy problem for harmonic maps defined on two-dimensional Minkowski space

1980 ◽  
Vol 33 (6) ◽  
pp. 727-737 ◽  
Author(s):  
Gu Chao-Hao
Keyword(s):  
Cauchy Problem ◽  
Minkowski Space ◽  
Harmonic Maps ◽  
Two Dimensional ◽  
Dimensional Minkowski Space ◽  
The Cauchy Problem

Local existence with low regularity for the 2D compressible Euler equations

2021 ◽  
Vol 18 (03) ◽  
pp. 701-728
Author(s):  
Huali Zhang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Euler Equations ◽  
Local Existence ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
Spatial Derivative ◽  
Compressible Euler ◽  
The Cauchy Problem ◽  
Local Solutions

We prove the local existence, uniqueness and stability of local solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial data of velocity, density, specific vorticity [Formula: see text] and the spatial derivative of specific vorticity [Formula: see text].

The two-dimensional minkowski space fermion determinant by example

1988 ◽  
Vol 211 (1-2) ◽  
pp. 107-110 ◽  
Author(s):  
D. Cangemi ◽  
M. Makowka ◽  
G. Wanders
Keyword(s):  
Minkowski Space ◽  
Two Dimensional ◽  
Dimensional Minkowski Space

scholarly journals Regularization and Error Estimate for the Poisson Equation with Discrete Data

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 422
Author(s):  
Nguyen Anh Triet ◽  
Nguyen Duc Phuong ◽  
Van Thinh Nguyen ◽  
Can Nguyen-Huu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Poisson Equation ◽  
Regularization Method ◽  
Random Noise ◽  
Two Dimensional ◽  
The Poisson Equation ◽  
The Cauchy Problem ◽  
Ill Posed ◽  
Dimensional Domain

In this work, we focus on the Cauchy problem for the Poisson equation in the two dimensional domain, where the initial data is disturbed by random noise. In general, the problem is severely ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the data. To regularize the instable solution of the problem, we have applied a nonparametric regression associated with the truncation method. Eventually, a numerical example has been carried out, the result shows that our regularization method is converged; and the error has been enhanced once the number of observation points is increased.

scholarly journals Continuation and uniqueness for generalised Emden-Fowler systems

1991 ◽  
Vol 33 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Lynn H. Erbe ◽  
Zhongchao Liang
Keyword(s):  
Cauchy Problem ◽  
Differential System ◽  
Two Dimensional ◽  
The Cauchy Problem

AbstractWe discuss uniqueness and continuation of solutions to the Cauchy problem for a two dimensional Emden-Fowler differential system.

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