6 citations · 10 across the 10 of their papers we have counts for
10 papers
Singular stationary Navier-Stokes flows: examples and stability
Zachary Bradshaw, Dakota Palmer
Landau solutions, when oriented along the vertical axis, represent a one parameter family of exact, self-similar, axisymmetric, swirl-free solutions to the 3D stationary Navier-Sto…
Time asymptotics, time regularity and separation rates for Navier-Stokes flows in supercritical solution classes
Zachary Bradshaw, Joshua Hudson
This paper extends the weak solution theory for the 3D Navier-Stokes equations of Barker, Seregin and Sverak from a critical setting to a supercritical setting making sure to inclu…
Regularity, uniqueness and the relative size of small and large scales in SQG flows
Zachary Akridge, Zachary Bradshaw
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…
Asymptotic properties of discretely self-similar Navier-Stokes solutions with rough data
Zachary Bradshaw, Patrick Phelps
In this paper we explore the extent to which discretely self-similar (DSS) solutions to the 3D Navier-Stokes equations with rough data almost have the same asymptotics as DSS flows…
Asymptotic stability for the 3D Navier-Stokes equations in and nearby spaces
Zachary Bradshaw, Weinan Wang
We provide a short proof of -asymptotic stability around vector fields that are small in weak-, including small Landau solutions. We show that asymptotic stability also h…
Remarks on the separation of Navier-Stokes flows
Zachary Bradshaw
Recently, strong evidence has accumulated that some solutions to the Navier-Stokes equations in physically meaningful classes are not unique. The primary purpose of this paper is t…
Estimation of non-uniqueness and short-time asymptotic expansions for Navier-Stokes flows
Zachary Bradshaw, Patrick Phelps
There is considerable evidence that solutions to the non-forced 3D Navier-Stokes equations in the natural energy space are not unique. Assuming this is the case, it becomes importa…
Spatial decay of discretely self-similar solutions to the Navier-Stokes equations
Zachary Bradshaw, Patrick Phelps
Forward self-similar and discretely self-similar weak solutions of the Navier-Stokes equations are known to exist globally in time for large self-similar and discretely self-simila…
Remarks on sparseness and regularity of Navier-Stokes solutions
Dallas Albritton, Zachary Bradshaw
The goal of this paper is twofold. First, we give a simple proof that sufficiently sparse Navier--Stokes solutions do not develop singularities. This provides an alternative to the…
Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries
Dallas Albritton, Zachary Bradshaw
We develop a theory of self-similar solutions to the critical surface quasi-geostrophic equations. We construct self-similar solutions for arbitrarily large data in various regular…