14 citations · 38 across the 12 of their papers we have counts for
14 papers
The structure of weak solutions to the Navier-Stokes equations
Zachary Bradshaw, Igor Kukavica
The existence of superfluous solutions to the Navier-Stokes equations in the whole space implies that not all solutions with uniformly locally bounded energy satisfy a useful local…
Global Navier-Stokes flows in intermediate spaces
Zachary Bradshaw, Misha Chernobai, Tai-Peng Tsai
We construct global weak solutions of the three dimensional incompressible Navier-Stokes equations in intermediate spaces between the space of uniformly locally square integrable f…
Mild solutions and spacetime integral bounds for Stokes and Navier-Stokes flows in Wiener amalgam spaces
Zachary Bradshaw, Chen-Chih Lai, Tai-Peng Tsai
We first prove decay estimates and spacetime integral bounds for Stokes flows in amalgam spaces which connect the classical Lebesgue spaces to the spaces of uniformly local…
Global weak solutions of the Navier-Stokes equations for intermittent initial data in half-space
Zachary Bradshaw, Igor Kukavica, Wojciech S. Ożański
We prove existence of global-in-time weak solutions of the incompressible Navier-Stokes equations in the half-space with initial data in a weighted space that allo…
Local energy solutions to the Navier-Stokes equations in Wiener amalgam spaces
Zachary Bradshaw, Tai-Peng Tsai
We establish existence of solutions in a scale of classes weaker than the finite energy Leray class and stronger than the infinite energy Lemarié-Rieusset class. The new classes ar…
On the local pressure expansion for the Navier-Stokes equations
Zachary Bradshaw, Tai-Peng Tsai
We show that the pressure associated with a distributional solution of the Navier-Stokes equations on the whole space satisfies a local expansion defined as a distribution if and o…
Existence of global weak solutions to the Navier-Stokes equations in weighted spaces
Zachary Bradshaw, Igor Kukavica, Tai-Peng Tsai
We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of data allowing growth at spatial infinity. Namely, we show the global exi…
Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations
Zachary Bradshaw, Tai-Peng Tsai
This paper addresses several problems associated to local energy solutions (in the sense of Lemarié-Rieusset) to the Navier-Stokes equations with initial data which is sufficiently…
Self-similar solutions to the Navier-Stokes equations: a survey of recent results
Zachary Bradshaw, Tai-Peng Tsai
We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an e…
Discretely self-similar solutions to the Navier-Stokes equations with data in satisfying the local energy inequality
Zachary Bradshaw, Tai-Peng Tsai
Chae and Wolf recently constructed discretely self-similar solutions to the Navier-Stokes equations for any discretely self similar data in . Their solutions ar…
Discretely self-similar solutions to the Navier-Stokes equations with Besov space data
Zachary Bradshaw, Tai-Peng Tsai
We construct self-similar solutions to the three dimensional Navier-Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space $\…
Rotationally corrected scaling invariant solutions to the Navier-Stokes equations
Zachary Bradshaw, Tai-Peng Tsai
We introduce new classes of solutions to the three dimensional Navier-Stokes equations in the whole and half spaces that add rotational correction to self-similar and discretely se…
Forward discretely self-similar solutions of the Navier-Stokes equations II
Zachary Bradshaw, Tai-Peng Tsai
For any discretely self-similar, incompressible initial data which satisfies where is allowed to be large, we construct a forwar…
Forward Discretely Self-Similar Solutions of the Navier-Stokes Equations
Tai-Peng Tsai
Extending the work of Jia and Sverak on self-similar solutions of the Navier-Stokes equations, we show the existence of large, forward, discretely self-similar solutions.