5 citations · 11 across the 6 of their papers we have counts for
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Finite time singularities in the Landau equation with very hard potentials
Jacob Bedrossian, Jiajie Chen, Maria Pia Gualdani +3
We consider the inhomogeneous Landau equation with and construct smooth, strictly positive initial data that develop a finite time singularity. The -norm o…
A new type of stable shock formation in gas dynamics
Isaac Neal, Calum Rickard, Steve Shkoller +1
From an open set of initial data, we construct a family of classical solutions to the 1D nonisentropic compressible Euler equations which form cusps as a first singularit…
A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy
Isaac Neal, Steve Shkoller, Vlad Vicol
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…
Holder Continuous Solutions of Active Scalar Equations
Philip Isett, Vlad Vicol
We consider active scalar equations , where is a divergence-free velocity field, and is a Fourier multiplier operator with s…
On the inviscid limit of the Navier-Stokes equations
Peter Constantin, Igor Kukavica, Vlad Vicol
We consider the convergence in the norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary condit…
The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half Space
Igor Kukavica, Vlad Vicol
We address the problem of analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-analyticity radius of…