Results 11 to 20 of about 717,764 (281)

A priori estimates for fluid interface problems [PDF]

Communications on Pure and Applied Mathematics, 2008
AbstractWe consider the regularity of an interface between two incompressible and inviscid fluid flows in the presence of surface tension. We obtain local‐in‐time estimates on the interface in H(3/2)k + 1 and the velocity fields in H(3/2)k. These estimates are obtained using geometric considerations which show that the Kelvin‐Helmholtz instabilities ...
Shatah, Jalal, Zeng, Chongchun
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Numerical resolution of the wave equation using the spectral method

Boundary Value Problems, 2022
We present a new procedure for the numerical study of the wave equation. We use the spectral discretization method associated with the Euler scheme for spatial and temporal discretization. A detailed numerical analysis leads to an a priori error estimate.
Mohamed Abdelwahed, Nejmeddine Chorfi
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On some properties of traveling water waves with vorticity [PDF]

, 2008
We prove that for a large class of vorticity functions the crests of any corresponding traveling gravity water wave of finite depth are necessarily points of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure
Varvaruca, Eugen
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Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution

Mathematics, 2023
The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved.
Victor Orlov
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A Priori Estimates or Elliptic Systems

Zeitschrift für Analysis und ihre Anwendungen, 1987
A priori estimates for the general complex Beltrami equation in connection with Riemann–Hilbert boundary conditions are developed, which can be used for existence as well as uniqueness statements for related nonlinear problems. For this reason the equation together with the boundary conditions are transformed into the canonical form and essentially a ...
Begehr, H., Hsiao, G. C.
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A PRIORI ESTIMATE FOR AN EQUATION WITH FRACTIONAL DERIVATIVES WITH DIFFERENT ORIGINS [PDF]

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2019
We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media.
L. M. Eneeva
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Banach space projections and Petrov-Galerkin estimates [PDF]

, 2015
We sharpen the classic a priori error estimate of Babuska for Petrov-Galerkin methods on a Banach space. In particular, we do so by (i) introducing a new constant, called the Banach-Mazur constant, to describe the geometry of a normed vector space; (ii ...
Stern, Ari
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A priori estimates for complex Hessian equations [PDF]

Analysis & PDE, 2014
We prove some $L^{\infty}$ a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of $C^n$ and on compact K hler manifolds. We also show optimal $L^p$ integrability for m-subharmonic functions with compact singularities, thus partially confirming a conjecture of Blocki. Finally
Dinew, Sławomir, Kołodziej, Sławomir
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Infinitely many sign-changing solutions for a semilinear elliptic equation with variable exponent

AIMS Mathematics, 2021
This paper is devoted to study a class of semilinear elliptic equations with variable exponent. By means of perturbation technique, variational methods and a priori estimation, the existence of infinitely many sign-changing solutions to this class of ...
Changmu Chu, Yuxia Xiao , Yanling Xie
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A local regularity for the complex Monge-Amp\`ere equation [PDF]

, 2010
We prove a local regularity (and a corresponding a priori estmate) for plurisubharmonic solutions of the nondegenerate complex Monge-Amp\'ere equation assuming that their $W^{2,p}$-norm is under control for some $p>n(n-1)$. This condition is optimal.
Blocki, Zbigniew, Dinew, Slawomir
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