Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Albritton, Dallas"'
The physical quantities in a gas should vary continuously across a shock. However, the physics inherent in the compressible Euler equations is insufficient to describe the width or structure of the shock. We demonstrate the existence of weak shock pr
Externí odkaz:
http://arxiv.org/abs/2402.01581
Autor:
Albritton, Dallas, Ożański, Wojciech
We consider vortex column solutions $v = V(r) e_\theta + W(r) e_z$ to the $3$D Euler equations. We give a mathematically rigorous construction of the countable family of unstable modes discovered by Liebovich and Stewartson (J. Fluid Mech. 126, 1983)
Externí odkaz:
http://arxiv.org/abs/2310.20674
Autor:
Albritton, Dallas, Ogden, W. Jacob
We consider a complexification of the Euler equations introduced by \v{S}ver\'ak which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analytic regularity and, moreover, we exhibit solutions which lose an
Externí odkaz:
http://arxiv.org/abs/2310.03120
Autor:
Albritton, Dallas, De Nitti, Nicola
We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admissible by the $L^\infty$ and total variation bounds and viscosity. This
Externí odkaz:
http://arxiv.org/abs/2308.06586
We give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier-Stokes equations with non-zero boundary conditions. It is inspired by an analogous approach for the stationary sy
Externí odkaz:
http://arxiv.org/abs/2211.16188
Autor:
Albritton, Dallas, Colombo, Maria
We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike the solutions constructed in \cite{albritton2021non}, the solutions we construct live at a supercritical scaling, in which the
Externí odkaz:
http://arxiv.org/abs/2209.08713
We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-uniqueness discovered by the authors in [1].
Comment: Final versi
Comment: Final versi
Externí odkaz:
http://arxiv.org/abs/2209.03530
Autor:
Albritton, Dallas, Ohm, Laurel
We consider a kinetic model of an active suspension of rod-like microswimmers. In certain regimes, swimming has a stabilizing effect on the suspension. We quantify this effect near homogeneous isotropic equilibria $\overline{\psi} = \text{const}$. No
Externí odkaz:
http://arxiv.org/abs/2205.04922
We establish a local-in-space short-time smoothing effect for the Navier-Stokes equations in the half space. The whole space analogue, due to Jia and \v{S}ver\'ak [J\v{S}14], is a central tool in two of the authors' recent work on quantitative $L^3_x
Externí odkaz:
http://arxiv.org/abs/2112.10705
Autor:
Albritton, Dallas, Brué, Elia, Colombo, Maria, De Lellis, Camillo, Giri, Vikram, Janisch, Maximilian, Kwon, Hyunju
In this expository work, we present Vishik's theorem on non-unique weak solutions to the two-dimensional Euler equations on the whole space, \[ \partial_t \omega + u \cdot \nabla \omega = f \, , \quad u = \frac{1}{2\pi} \frac{x^\perp}{|x|^2} \ast \om
Externí odkaz:
http://arxiv.org/abs/2112.04943