Results 31 to 40 of about 160 (57)

The Stokes and Poisson problem in variable exponent spaces [PDF]

Com. Var. Ell. Equ. 56, No.7-9, 789 - 811, 2011, 2012
We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove the existence of strong and weak solutions for bounded domains with C^{1,1} boundary with inhomogenous boundary values. The result is based on generalizations of the classical theories of Calderon-Zygmund and Agmon-Douglis-Nirenberg to variable exponent spaces.
arxiv   +1 more source

Some aspects of anisotropic curvature flow of planar partitions [PDF]

arXiv, 2023
We consider the geometric evolution of a network in the plane, flowing by anisotropic curvature. We discuss local existence of a classical solution in the presence of several smooth anisotropies. Next, we discuss some aspects of the polycrystalline case.
arxiv  

Euler-α equations in a three-dimensional bounded domain with Dirichlet boundary conditions

Open Mathematics
In this article, we investigate the Euler-α\alpha equations in a three-dimensional bounded domain. On the one hand, we prove in the Euler setting that the equations are locally well-posed with initial data in Hs(s≥3){H}^{s}\left(s\ge 3).
Yuan Shaoliang, Huang Lehui, Cheng Lin, You Xiaoguang   +3 more
doaj   +1 more source

A regularity result for incompressible elastodynamics equations in the ALE coordinates

Advanced Nonlinear Studies
We consider incompressible inviscid elastodynamics equations with a free surface and establish regularity of solutions for these equations. Compared with previous result on this free boundary problem [X. Gu and F.
Xie Binqiang
doaj   +1 more source

On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source [PDF]

Archive for Rational Mechanics and Analysis 223 (2017), 1183-1237, 2015
The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for initial data in the natural energy space. Moreover the regularity of solutions is studied. Finally a dynamical system is generated when sources are at most linear at infinity,
arxiv   +1 more source

On a new transformation for generalised porous medium equations: from weak solutions to classical [PDF]

arXiv, 2014
It is well-known that solutions for generalised porous medium equations are, in general, only H\"older continuous. In this note, we propose a new variable substitution for such equations which transforms weak solutions into classical.
arxiv  

Global regularity properties of steady shear thinning flows [PDF]

arXiv, 2016
In this paper we study the regularity of weak solutions to systems of p-Stokes type, describing the motion of some shear thinning fluids in certain steady regimes. In particular we address the problem of regularity up to the boundary improving previous results especially in terms of the allowed range for the parameter p.
arxiv  

Maximal $L^p$-$L^q$ regularity for the Stokes problem with Navier-type boundary conditions [PDF]

arXiv, 2017
Maximal $L^p$-$L^q$ regularity is proved for the strong, weak and very weak solutions of the inhomogeneous Stokes problem with Navier-type boundary conditions in a bounded domain $\Omega$, not necessarily simply connected. This extends previous results of the authors (2017).
arxiv  

Local well-posedness of the Hall-MHD system in $H^s(\mathbb {R}^n)$ with $s>\frac n2$ [PDF]

arXiv, 2017
We establish local well-posedness of the Hall-magneto-hydrodynamics (Hall-MHD) system in the Sobolev space $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2$. The previously known local well-posedness space was $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2+1$. Thus the result presented here is an improvement.
arxiv  

Global dissipative half-harmonic flows into spheres: small data in critical Sobolev spaces [PDF]

arXiv, 2018
We establish global existence, uniqueness, regularity and long-time asymptotics of strong solutions to the half-harmonic heat flow and dissipative Landau-Lifshitz equation, valid for initial data that is small in the homogeneous Sobolev norm $\dot{H}^{\frac n 2}$ for space dimensions $n \le 3$.
arxiv