Zobrazeno 1 - 10
of 263
pro vyhledávání: '"Vicol, Vlad"'
We prove finite-time vorticity blowup for smooth solutions of the 2D compressible Euler equations with smooth, localized, and non-vacuous initial data. The vorticity blowup occurs at the time of the first singularity, and is accompanied by an axisymm
Externí odkaz:
http://arxiv.org/abs/2407.06455
Autor:
Shkoller, Steve, Vicol, Vlad
We construct a fundamental piece of the boundary of the maximal globally hyperbolic development (MGHD) of Cauchy data for the multi-dimensional compressible Euler equations, which is necessary for the local shock development problem. For an open set
Externí odkaz:
http://arxiv.org/abs/2310.08564
Autor:
Armstrong, Scott, Vicol, Vlad
For every $\alpha < 1/3$, we construct an explicit divergence-free vector field $\mathbf{b}(t,x)$ which is periodic in space and time and belongs to $C^0_t C^{\alpha}_x \cap C^{\alpha}_t C^0_x$ such that the corresponding scalar advection-diffusion e
Externí odkaz:
http://arxiv.org/abs/2305.05048
From an open set of initial data, we construct a family of classical solutions to the 1D nonisentropic compressible Euler equations which form $C^{0,\nu}$ cusps as a first singularity, for any $\nu \in [1/2,1)$. For this range of $\nu$, this is the f
Externí odkaz:
http://arxiv.org/abs/2303.16842
We provide a detailed analysis of the shock formation process for the non-isentropic 2d Euler equations in azimuthal symmetry. We prove that from an open set of smooth and generic initial data, solutions of Euler form a first singularity or gradient
Externí odkaz:
http://arxiv.org/abs/2302.01289
Autor:
Novack, Matthew, Vicol, Vlad
For any regularity exponent $\beta<\frac 12$, we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class $C^0_t (H^{\beta} \cap L^{\frac{1}{(1-2\beta)}})$. By interpolation, such solutions belong to $C^0_tB^{s}
Externí odkaz:
http://arxiv.org/abs/2203.13115
We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null controllable, i.e., can be driven to the zero
Externí odkaz:
http://arxiv.org/abs/2108.12089
We establish the validity of the Euler$+$Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boun
Externí odkaz:
http://arxiv.org/abs/2107.03417
A fundamental question in fluid dynamics concerns the formation of discontinuous shock waves from smooth initial data. We prove that from smooth initial data, smooth solutions to the 2d Euler equations in azimuthal symmetry form a first singularity,
Externí odkaz:
http://arxiv.org/abs/2106.02143
We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, contain a cubic nonlinearity, and yet have a favorable $L^2$ energy stru
Externí odkaz:
http://arxiv.org/abs/2104.14084