5 citations · 13 across the 12 of their papers we have counts for
12 papers
Homothetic Self-Similar Solutions to the Incompressible Navier-Stokes Equations
Tim Binz, Matei P. Coiculescu
We investigate homothetic forward self-similar solutions of the incompressible Navier-Stokes equations: the solutions for which both and $β\overline{U…
Multi-Sink Solutions to the Self-Similar Euler Equations
Hyungjun Choi, Matei P. Coiculescu
We construct examples and provide a classification of self-similar solutions to the two-dimensional incompressible Euler equations whose pseudo-velocity fields possess more than on…
Conditional Liouville theorems for the Navier-Stokes equations
Matei P. Coiculescu, Jincheng Yang
We present a novel approach to the Liouville problem for the stationary Navier-Stokes equations. As an application of our method, we prove conditional Liouville theorems with assum…
Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data
Matei P. Coiculescu, Stan Palasek
We consider the Cauchy problem for the incompressible Navier-Stokes equations in dimension three and construct initial data in the critical space from which there exist…
Stability of the Inviscid Power-Law Vortex
Tim Binz, Matei P. Coiculescu
We prove that the power-law vortex , which explicitly solves the stationary unforced incompressible Euler equations in in both physical an…
Partial Regularity and Blowup for an Averaged Three-Dimensional Navier-Stokes Equation
Matei P. Coiculescu
We prove two results that together strongly suggest that obtaining a positive answer to the Navier-Stokes global regularity question requires more than a refinement of partial regu…
An Application of the Theory of Viscosity Solutions to Higher Order Differential Equations
Matei P. Coiculescu
We directly apply the theory of viscosity solutions to partial differential equations of order greater than two. We prove that there exists a solution in $C^{2,α}(B_R)\cap C(\overl…
The Affine Shape of a Figure-Eight under the Curve Shortening Flow
Matei P. Coiculescu, Richard Evan Schwartz
We consider the curve shortening flow applied to a class of figure-eight curves: those with dihedral symmetry, convex lobes, and a monotonicity assumption on the curvature. We prov…
Some New Results in Geometric Analysis
Matei P. Coiculescu
This thesis presents three results in geometric analysis. We first analyze the curve-shortening flow on figure eight curves in the plane. Afterwards, we examine the point-wise curv…
Stationary Solutions of the Curvature Preserving Flow on Space Curves
Matei P. Coiculescu
We study a geometric flow on curves, immersed in , that have strictly positive torsion. The evolution equation is given by where…
An Interpolation from Sol to Hyperbolic Space
Matei P. Coiculescu
We study a one-parameter family of nonisomorphic solvable Lie groups, which, when equipped with canonical left-invariant metrics, becomes an i…
The Spheres of Sol
Matei P. Coiculescu, Richard Evan Schwartz
Let Sol be the three-dimensional solvable Lie group equipped with its standard left-invariant Riemannian metric. We give a precise description of the cut locus of the identity, and…