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pro vyhledávání: '"35d35"'
Autor:
Fino, Ahmad Z., Hamza, Mohamed Ali
This paper addresses the Cauchy problem for wave equations with scale-invariant time-dependent damping and nonlinear time-derivative terms, modeled as $$\partial_{t}^2u- \Delta u +\frac{\mu}{1+t}\partial_tu= f(\partial_tu), \quad x\in \mathbb{R}^n, t
Externí odkaz:
http://arxiv.org/abs/2409.13353
In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are proved with t
Externí odkaz:
http://arxiv.org/abs/2408.17144
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a diffuse in
Externí odkaz:
http://arxiv.org/abs/2408.07449
In this paper, we present an analysis of the Kelvin-Helmholtz instability in two-dimensional ideal compressible elastic flows, providing a rigorous confirmation that weak elasticity has a destabilizing effect on the Kelvin-Helmholtz instability. Ther
Externí odkaz:
http://arxiv.org/abs/2408.00053
A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard energy with a singular (logarithmic) potential short time well-posedn
Externí odkaz:
http://arxiv.org/abs/2407.14941
Autor:
Kim, Jongmyeong, Lee, Se-Chan
We prove the Aleksandrov--Bakelman--Pucci estimate for non-uniformly elliptic equations in non-divergence form. Moreover, we investigate local behaviors of solutions of such equations by developing local boundedness and weak Harnack inequality. Here
Externí odkaz:
http://arxiv.org/abs/2406.18250
Autor:
Gkikas, Konstantinos T.
Let $N\geq 2$ and $F:\mathbb{R}^N\to \mathbb{R} $ be the unique increasing radially symmetric function satisfying the minimal surface equation for graphs with the initial conditions $F(1)=0$ and $\lim_{r\to 1}F_r(r)=\infty;$ $r=|x|.$ We construct an
Externí odkaz:
http://arxiv.org/abs/2406.10530
In this paper, we derive decay rates of the solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak solutions of these equations by refining the Fourier splitting method
Externí odkaz:
http://arxiv.org/abs/2404.16290
In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravity). We prove global well-posedness for the corresponding Hamilton-Jaco
Externí odkaz:
http://arxiv.org/abs/2404.10972
Autor:
Song, Zihao
We consider the global well-posedness and decay rates for solutions of 3D incompressible micropolar equation in the critical Besov space. Spectrum analysis allows us to find not only parabolic behaviors of solutions, but also damping effect of angula
Externí odkaz:
http://arxiv.org/abs/2404.08920