Results 101 to 110 of about 36,597 (202)

Well-posedness of one-dimensional Korteweg models

Electronic Journal of Differential Equations, 2006
We investigate the initial-value problem for one-dimensional compressible fluids endowed with internal capillarity. We focus on the isothermal inviscid case with variable capillarity.
Sylvie Benzoni-Gavage, Raphael Danchin, Stephane Descombes   +2 more
doaj  

Cut Finite Element 3D Acoustic Shape Optimization of a Compression Driver Taking Viscothermal Losses Into Account

International Journal for Numerical Methods in Engineering, Volume 127, Issue 4, 28 February 2026.
ABSTRACT Wave propagation effects such as resonance and interference effects complicate the design of many acoustic devices, particularly when the dimensions of the device are in the order of the operating wavelength. At the same time, these complications also offer an opportunity for numerical optimization schemes to outperform designs achieved using ...
Martin Berggren, Anders Bernland, André Massing, Daniel Noreland, Eddie Wadbro   +4 more
wiley   +1 more source

Ill-posedness for periodic nonlinear dispersive equations

Electronic Journal of Differential Equations, 2010
In this article, we establish new results about the ill-posedness of the Cauchy problem for the modified Korteweg-de Vries and the defocusing modified Korteweg-de Vries equations, in the periodic case. The lack of local well-posedness is in the sense
Jaime Angulo Pava, Sevdzhan Hakkaev
doaj  

The Periodic Boundary Value Problem for the Weakly Dissipative μ-Hunter-Saxton Equation

Advances in Mathematical Physics, 2015
We study the periodic boundary value problem for the weakly dissipative μ-Hunter-Saxton equation. We establish the local well-posedness in Besov space B2,13/2, which extends the previous regularity range to the critical case.
Zhengyong Ouyang, Xiangdong Wang, Haiwu Rong   +2 more
doaj   +1 more source

Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems

Electronic Journal of Differential Equations, 2003
This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks ...
Hailiang Li, Chi-Kun Lin
doaj  

On the Global Well-Posedness of the Viscous Two-Component Camassa-Holm System

Abstract and Applied Analysis, 2012
We establish the local well-posedness for the viscous two-component Camassa-Holm system. Moreover, applying the energy identity, we obtain a global existence result for the system with (u0,η0)∈H1(ℝ)×L2(ℝ).
Xiuming Li
doaj   +1 more source

Remark on well-posedness and ill-posedness for the KdV equation

Electronic Journal of Differential Equations, 2010
We consider the Cauchy problem for the KdV equation with low regularity initial data given in the space $H^{s,a}(mathbb{R})$, which is defined by the norm $$ | varphi |_{H^{s,a}}=| langle xi angle^{s-a} |xi|^a widehat{varphi} |_{L_{xi}^2}.
Takamori Kato
doaj  

On well-posedness of energy supercritical NLS on product space Rn×T4−n ${\mathbb{R}}^{n}{\times}{\mathbb{T}}^{4-n}$ (n = 0, 1, 2, 3)

Advances in Nonlinear Analysis
We establish the well-posedness theory for the quintic nonlinear Schrödinger equation (NLS) on four-dimensional tori (i.e., T4 ${\mathbb{T}}^{4}$ ), which is an energy-supercritical model. Compared to the recent breakthrough work (B. Kwak and S.
Wang Han, Li Xing, Lyu Ziyue, Zhao Zehua, Zhou Wenyu   +4 more
doaj   +1 more source

Improved well-posedness for quasilinear and sharp local well-posedness for semilinear KP-I equations

72 ...
Kinoshita, Shinya, Sanwal, Akansha, Schippa, Robert   +2 more
openaire   +2 more sources

On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations

Electronic Journal of Differential Equations, 2009
The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation $$ u_t + u_{xxx} + partial_x^{-1}u_{yy}= (u^l)_x, quad l ge 3, $$ is shown to be locally well-posed in almost critical anisotropic Sobolev spaces.
Axel Gruenrock
doaj