scholarly journals On the motion of a rigid body in a two-dimensional ideal flow with vortex sheet initial data

2013 ◽  
Vol 30 (3) ◽  
pp. 401-417 ◽  
Author(s):  
Franck Sueur
Keyword(s):  
Initial Data ◽  
Rigid Body ◽  
Vortex Sheet ◽  
Two Dimensional ◽  
Ideal Flow

scholarly journals On the Motion of a Rigid Body in a Two-Dimensional Irregular Ideal Flow

2012 ◽  
Vol 44 (5) ◽  
pp. 3101-3126 ◽  
Author(s):  
Olivier Glass ◽  
Franck Sueur
Keyword(s):  
Rigid Body ◽  
Two Dimensional ◽  
Ideal Flow

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].

scholarly journals The Limit $\alpha \to 0$ of the $\alpha$-Euler Equations in the Half-Plane with No-Slip Boundary Conditions and Vortex Sheet Initial Data

2020 ◽  
Vol 52 (5) ◽  
pp. 5257-5286
Author(s):  
Adriana V. Busuioc ◽  
Dragos Iftimie ◽  
Milton D. Lopes Filho ◽  
Helena J. Nussenzveig Lopes
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Euler Equations ◽  
Half Plane ◽  
Vortex Sheet ◽  
Slip Boundary Conditions ◽  
Slip Boundary

scholarly journals On the correctness of mathematical models of time-of-flight cathodoluminescence of direct-gap semiconductors

2019 ◽  
Vol 30 ◽  
pp. 07014
Author(s):  
Mikhail A. Stepovich ◽  
Dmitry V. Turtin ◽  
Elena V. Seregina ◽  
Veronika V. Kalmanovich
Keyword(s):  
Electron Beam ◽  
Gallium Nitride ◽  
Initial Data ◽  
Mathematical Models ◽  
Single Crystal ◽  
Three Dimensional ◽  
Time Of Flight ◽  
Semiconductor Material ◽  
Two Dimensional ◽  
Cathodoluminescence Intensity

Two-dimensional and three-dimensional mathematical models of diffusion and cathodoluminescence of excitons in single-crystal gallium nitride excited by a pulsating sharply focused electron beam in a homogeneous semiconductor material are compared. The correctness of these models has been carried out, estimates have been obtained to evaluate the effect of errors in the initial data on the distribution of the diffusing excitons and the cathodoluminescence intensity.

Immediate smoothing and global solutions for initial data in L1 × W1,2 in a Keller–Segel system with logistic terms in 2D

2020 ◽  
pp. 1-21
Author(s):  
Johannes Lankeit
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Two Dimensional ◽  
Image Position

This paper deals with the logistic Keller–Segel model \[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ v_t = \Delta v - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous Neumann boundary conditions and for parameters χ, κ ∈ ℝ and μ > 0), and shows that any nonnegative initial data (u0, v0) ∈ L1 × W1,2 lead to global solutions that are smooth in $\bar {\Omega }\times (0,\infty )$ .

Long Time Computation of Two-Dimensional Vortex Sheet by Point Vortex Method

2003 ◽  
Vol 72 (8) ◽  
pp. 1968-1976 ◽  
Author(s):  
Sun-Chul Kim ◽  
June-Yub Lee ◽  
Sung-Ik Sohn
Keyword(s):  
Point Vortex ◽  
Vortex Method ◽  
Vortex Sheet ◽  
Two Dimensional ◽  
Long Time

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.

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