Zobrazeno 1 - 10
of 117 894
pro vyhledávání: '"Mathematics - Analysis of PDEs"'
Autor:
Cao, Ruijia, Schäfer, Florian
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the deformation map
Externí odkaz:
http://arxiv.org/abs/2411.15121
Autor:
McConnell, Ryan, Oh, Seungly
We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $H^s(\mathbb{T})$ for $s> -\frac23$. This work creates an analogue of the mKdV result by Nakanishi, Takaoka, and T
Externí odkaz:
http://arxiv.org/abs/2411.15069
Autor:
Needham, David John, Billingham, John
In the third part of this series of papers, we address the same Cauchy problem that was considered in part 1, namely the nonlocal Fisher-KPP equation in one spatial dimension, $u_t = D u_{xx} + u(1-\phi_T*u)$, where $\phi_T*u$ is a spatial convolutio
Externí odkaz:
http://arxiv.org/abs/2411.15054
Autor:
Marra, Mateus, Smania, Daniel
Given two H\"older potentials $\phi_+$ and $\psi_-$ for the unilateral shift, we define anisotropic Banach spaces of distributions on the bilateral shift space with a finite alphabet. On these spaces, the transfer operator for the bilateral shift is
Externí odkaz:
http://arxiv.org/abs/2411.15050
Autor:
Akridge, Zachary, Bradshaw, Zachary
The problem of regularity and uniqueness are open for the supercritically dissipative surface quasi-geostrophic equations in certain classes. In this note we examine the extent to which small or large scales are necessarily active both for the temper
Externí odkaz:
http://arxiv.org/abs/2411.15040
Autor:
Marchese, Andrea, Merlo, Andrea
We give a new, elementary proof of the fact that metric 1-currents in the Euclidean space correspond to Federer-Fleming flat chains.
Externí odkaz:
http://arxiv.org/abs/2411.15019
Autor:
De Masi, Luigi, Marchese, Andrea
We prove a refined version of the celebrated Lusin type theorem for gradients by Alberti, stating that any Borel vector field $f$ coincides with the gradient of a $C^1$ function $g$, outside a set $E$ of arbitrarily small Lebesgue measure. We replace
Externí odkaz:
http://arxiv.org/abs/2411.15012
A model for the generation of heat due to mechanical losses during acoustic wave propagation in a solid is considered in a Kelvin-Voigt type framework. In contrast to previous studies on related thermoviscoelastic models, in line with recent experime
Externí odkaz:
http://arxiv.org/abs/2411.14900
Recently, Jiang--Jiang (J. Differential Equations 282, 2021) showed the existence of unique strong solutions in spatial periodic domain (denoted by $\mathbb{T}^3$), whenever the elasticity coefficient is larger than the initial velocity perturbation
Externí odkaz:
http://arxiv.org/abs/2411.14882
Autor:
Vasylyeva, Nataliya
In the paper, we discuss the two-dimensional contact Muskat problem with zero surface tension of a free boundary. The initial shape of the unknown interface is a smooth simple curve which forms acute corners $\delta_{0}$ and $\delta_{1}$ with fixed b
Externí odkaz:
http://arxiv.org/abs/2411.14859