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Displaying 21 – 40 of 258

The Cauchy problem for coupled Yang-Mills and scalar fields in the Lorentz gauge

J. Ginibre, G. Velo (1982)

Annales de l'I.H.P. Physique théorique

The Cauchy problem for Hartree-Fock time-dependent equations

Sandro Zagatti (1992)

Annales de l'I.H.P. Physique théorique

The Cauchy problem for the coupled Klein-Gordon-Schrödinger system

Changxing Miao, Youbin Zhu (2006)

Annales Polonici Mathematici

We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method has an unnatural...

The Cauchy problem for the Gross–Pitaevskii equation

P. Gérard (2006)

Annales de l'I.H.P. Analyse non linéaire

The Cauchy problem for the homogeneous time-dependent Oseen system in $ℝ^{3}$ : spatial decay of the velocity

Paul Deuring (2013)

Mathematica Bohemica

We consider the homogeneous time-dependent Oseen system in the whole space $ℝ^{3}$ . The initial data is assumed to behave as $O (| x |^{- 1 - ϵ})$ , and its gradient as $O (| x |^{- 3 / 2 - ϵ})$ , when $| x |$ tends to infinity, where $ϵ$ is a fixed positive number. Then we show that the velocity $u$ decays according to the equation $| u (x, t) | = O (| x |^{- 1})$ , and its spatial gradient $\nabla_{x} u$ decreases with the rate ${| x |}^{- 3 / 2}$ , for $| x |$ tending to infinity, uniformly with respect to the time variable $t$ . Since these decay rates are optimal even in the stationary case, they should also be the best possible...

The Cauchy problem for the liquid crystals system in the critical Besov space with negative index

Sen Ming, Han Yang, Zili Chen, Ls Yong (2017)

Czechoslovak Mathematical Journal

The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space ${\dot{B}}_{p, 1}^{n / p - 1} (ℝ^{n}) \times {\dot{B}}_{p, 1}^{n / p} (ℝ^{n})$ with $n < p < 2 n$ is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed.

The Cauchy problem for the magneto-hydrodynamic system

Marco Cannone, Changxing Miao, Nicolas Prioux, Baoquan Yuan (2006)

Banach Center Publications

We study the uniqueness and regularity of Leray-Hopf's weak solutions for the MHD equations with dissipation and resistance in different frameworks. Using different kinds of space-time estimates in conjunction with the Littlewood-Paley-Bony decomposition, we present some general criteria of uniqueness and regularity of weak solutions to the MHD system, and prove the uniqueness and regularity criterion in the framework of mixed space-time Besov spaces by applying Tao's trichotomy method.

The Cauchy problem for the nonlinear Schrödinger Equation in H1.

Thierry Cazenave, Fred B. Weissler (1988)

Manuscripta mathematica

The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity

Riccardo Adami, Gianfausto Dell'Antonio, Rodolfo Figari, Alessandro Teta (2003)

Annales de l'I.H.P. Analyse non linéaire

The Cauchy problem for the two dimensional Euler–Poisson system

Dong Li, Yifei Wu (2014)

Journal of the European Mathematical Society

The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system....

The Cauchy problem for the Vlasov-Maxwell equations

Glassey, Robert T., Schaeffer, Jack (1989)

Portugaliae mathematica

The Cauchy problem for viscous shallow water equations.

Weike Wang, Chao-Jiang Xu (2005)

Revista Matemática Iberoamericana

In this paper we study the Cauchy problem for viscous shallow water equations. We work in the Sobolev spaces of index s > 2 to obtain local solutions for any initial data, and global solutions for small initial data.

The change in electric potential due to lightning

William W. Hager, Beyza Caliskan Aslan (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The expression for the...

The complementing condition and its role in a bifurcation theory applicable to nonlinear elasticity.

Negrón-Marrero, Pablo V., Montes-Pizarro, Errol (2011)

The New York Journal of Mathematics [electronic only]

The conditioning of the stiffness matrix for certain elements approximating the incompressibility condition in fluid dynamics.

W. Dörfler (1990/1991)

Numerische Mathematik

The coupled problem of a solid oscillating in a viscous fluid under the action of an elastic force.

Guda, S.A., Yudovich, V.I. (2007)

Sibirskij Matematicheskij Zhurnal

The cubic Szegő equation

Patrick Gérard, Sandrine Grellier (2010)

Annales scientifiques de l'École Normale Supérieure

We consider the following Hamiltonian equation on the $L^{2}$ Hardy space on the circle, $i \partial_{t} u = {Π (| u |}^{2} u),$ where $Π$ is the Szegő projector. This equation can be seen as a toy model for totally non dispersive evolution equations. We display a Lax pair structure for this equation. We prove that it admits an infinite sequence of conservation laws in involution, and that it can be approximated by a sequence of finite dimensional completely integrable Hamiltonian systems. We establish several instability phenomena illustrating...

Currently displaying 21 – 40 of 258