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Global existence of small amplitude solution to nonlinear system of wave and Klein-Gordon equations in four space-time dimensions
Global existence nonlinear system wave and Klein-Gordon equations four space-time dimensions
2011/9/14
Abstract: In this article one will develop a so-called hyperboloidal foliation method, which is an energy method based on a foliation of space-time into hyperboloidal hypersurfaces. This method permit...
Transport equations with fractal noise - existence, uniqueness and regularity of the solution
Stochastic partial differential equations Transport equation Nonsmooth coefficients Fractional Brownian noise
2011/9/15
Abstract: The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coe...
Generalized Ricci flow I: Local existence and uniqueness
Generalized Ricci flow uniformly parabolic system short-time existence Thurston’s eight geometries
2011/9/13
Abstract: In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that...
On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation
Generalized periodic Camassa-Holm equation Wave-breaking Global existence
2011/9/9
Abstract: Considered herein is the initial-value problem for the generalized periodic Camassa-Holm equation which is related to the Camassa-Holm equation and the Hunter-Saxton equation. Sufficient con...
On the existence of a time inhomogeneous skew Brownian motion and some related laws
time inhomogeneous skew Brownian motion Probability
2011/9/2
Abstract: This article is devoted to the construction of a solution for the "skew inhomogeneous Brownian motion" equation, which first appear in a seminal paper by Sophie Weinryb (1983). We investigat...
Existence of strong solutions in a larger space for the shallow-water system
the shallow-water system Analysis of PDEs
2011/9/5
Abstract: This paper is dedicated to the study of both viscous compressible barotropic fluids and Navier-Stokes equation with dependent density, when the viscosity coefficients are variable, in dimens...
Existence and computation of Riemann-Stieltjes integrals through Riemann integrals
Riemann-Stieltjes integrals Riemann integrals Classical Analysis and ODEs
2011/9/1
Abstract: We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by mean...
Global existence and collisions for symmetric configurations of nearly parallel vortex filaments
Global existence and collisions parallel vortex filaments Analysis of PDEs
2011/9/1
Abstract: We consider the Schr\"odinger system with Newton-type interactions that was derived by R. Klein, A. Majda and K. Damodaran [18] to modelize the dynamics of N nearly parallel vortex filaments...
Global existence for the Euler-Maxwell system
Global existence the Euler-Maxwell system Analysis of PDEs
2011/8/30
Abstract: The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existe...
Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption
Very singular solution singular diffusion gradient absorption self-similar solutions p-Laplacian uniqueness
2011/8/26
Abstract: Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption {equation*} \partial_t u -\Delta_{...
On the Local Existence for the Characteristic Initial Value Problem in General Relativity
Characteristic Initial Value Problem General Relativity Analysis of PDEs
2011/9/29
Abstract: Given a truncated incoming null cone and a truncated outgoing null cone intersecting at a two sphere $S$ with smooth characteristic initial data, a theorem of Rendall shows that the vacuum E...
Long time existence of the symplectic mean curvature flow
symplectic mean curvature flow Long time Differential Geometry
2011/8/25
Abstract: Let $(M,\bar{g})$ be a K\"ahler surface with a constant holomorphic sectional curvature $k>0$, and $\Sigma$ an immersed symplectic surface in $M$. Suppose $\Sigma$ evolves along the mean cur...
The global existence of the smoothing solution for the Navier-Stokes equations
smoothing solution Poisson’s equation heat-conduct equation the Schauder fixed-point theorem
2011/8/24
Abstract: This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four...
Existence of Minimizers of a class of multi-constrained variationnal problems in the absence of compactness, symmetry and monotonicity
Minimizers multi-constrained variationnal problems absence of compactness symmetry and monotonicity
2011/8/23
Abstract: We prove the existence of minimizers of a class of multi-constrained variational problems in which the non linearity involved does not sat- isfy compactness, monotonicity, neither symmetry p...
Existence and multiplicity of solutions to equations of $N-$Laplacian type with critical exponential growth in $\mathbb{R}^{N}$
Ekeland variational principle Mountain-pass Theorem Variational methods Critical growth Moser-Trudinger inequality
2011/8/23
Abstract: In this paper, we deal with the existence and multiplicity of solutions to the nonuniformly elliptic equation of the N-Lapalcian type with a potential and a nonlinear term of critical expone...