scholarly journals Regularizing Model for the 2D MHD Equations with Zero Viscosity

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Ensil Kang ◽  
Jihoon Lee
Keyword(s):  
Classical Solution ◽  
A Priori Estimates ◽  
A Priori ◽  
Mhd Equations ◽  
Two Dimensional ◽  
System A ◽  
Priori Estimates ◽  
Zero Viscosity ◽  
Time Existence ◽  
Hydrodynamics Equations

We consider the regularity of two dimensional incompressible magneto-hydrodynamics equations with zero viscosity. We provide an approximating system to the equations and prove global-in-time existence of classical solution to this approximating system. By using approximating system, a priori estimates for the equations can be justified.

A priori estimates of solutions of boundary value problems for two-dimensional systems of singular differential inequalities

2011 ◽  
Vol 18 (1) ◽  
pp. 163-175
Author(s):  
Nino Partsvania
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Differential Inequalities ◽  
Two Dimensional ◽  
Point Boundary ◽  
Estimates Of Solutions ◽  
Priori Estimates ◽  
Singular Coefficients

Abstract A priori estimates of solutions of two-point boundary value problems for two-dimensional systems of differential inequalities with singular coefficients are established.

scholarly journals ABSORBING BOUNDARY CONDITIONS FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH AN EXTERIOR POTENTIAL PART I: CONSTRUCTION AND A PRIORI ESTIMATES

2012 ◽  
Vol 22 (10) ◽  
pp. 1250026 ◽  
Author(s):  
XAVIER ANTOINE ◽  
CHRISTOPHE BESSE ◽  
PAULINE KLEIN
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
A Priori Estimates ◽  
Pseudodifferential Operators ◽  
A Priori ◽  
Absorbing Boundary Conditions ◽  
Two Dimensional ◽  
Absorbing Boundary ◽  
Priori Estimates

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.

scholarly journals The study of a mathematical model of surface reactions

2014 ◽  
Vol 55 ◽  
Author(s):  
Algirdas Ambrazevičius ◽  
Gintaras Puriuškis
Keyword(s):  
Mathematical Model ◽  
Carbon Monoxide ◽  
Nitrous Oxide ◽  
Differential Equations ◽  
Classical Solution ◽  
A Priori Estimates ◽  
Surface Reactions ◽  
A Priori ◽  
Coupled System ◽  
Priori Estimates

We prove the a priori estimates of a classical solution to a coupled system of parabolic and ordinary differential equations, the latter being determined on the boundary of the domain. This system describes the model of surface reactions between carbon monoxide and nitrous oxide.

scholarly journals Global existence of classical solutions to the two-dimensional compressible Boussinesq equations in a square domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xucheng Huang ◽  
Zhaoyang Shang ◽  
Na Zhang
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Boussinesq Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Priori Estimates ◽  
Constant Viscosity ◽  
Initial Boundary Value

Abstract In this paper, we consider the initial boundary value problem of two-dimensional isentropic compressible Boussinesq equations with constant viscosity and thermal diffusivity in a square domain. Based on the time-independent lower-order and time-dependent higher-order a priori estimates, we prove that the classical solution exists globally in time provided the initial mass $\|\rho _{0}\|_{L^{1}}$ ∥ ρ 0 ∥ L 1 of the fluid is small. Here, we have no small requirements for the initial velocity and temperature.

scholarly journals Regularity results for nonlocal evolution Venttsel’ problems

2020 ◽  
Vol 23 (5) ◽  
pp. 1416-1430 ◽  
Author(s):  
Simone Creo ◽  
Maria Rosaria Lancia ◽  
Alexander I. Nazarov
Keyword(s):  
Sobolev Spaces ◽  
Fractional Laplacian ◽  
A Priori Estimates ◽  
A Priori ◽  
Extension Theorem ◽  
Weighted Sobolev Spaces ◽  
Nonlocal Term ◽  
Two Dimensional ◽  
Priori Estimates ◽  
Regularity Results

Abstract We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution. The nonlocal term can be regarded as a regional fractional Laplacian on the boundary. The regularity results deeply rely on a priori estimates, obtained via the so-called Munchhausen trick, and sophisticated extension theorem for anisotropic weighted Sobolev spaces.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

2020 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Diffusion Parameter ◽  
Priori Estimates ◽  
De Vries ◽  
Wall Interactions

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

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