89 citations · 481 across the 52 of their papers we have counts for
52 papers · 1 filter
Large discretely self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field
Tai-Peng Tsai
Discretely self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field for large discretely self-similar initial data are constructed in this note, exte…
On linear elliptic equations with drift terms in critical weak spaces
Hyunseok Kim, Tuoc Phan, Tai-Peng Tsai
We study the Dirichlet problem for a second order linear elliptic equation in a bounded smooth domain in , , with the drift belonging to th…
Gradient estimates for the non-stationary Stokes system with the Navier boundary condition
Hui Chen, Su Liang, Tai-Peng Tsai
For the non-stationary Stokes system, it is well-known that one can improve spatial regularity in the interior, but not near the boundary if it is coupled with the no-slip boundary…
Growth rates for anti-parallel vortex tube Euler flows in three and higher dimensions
Stephen Gustafson, Evan Miller, Tai-Peng Tsai
We consider axisymmetric, swirl-free solutions of the Euler equations in three and higher dimensions, of generalized anti-parallel-vortex-tube-pair-type: the initial scalar vortici…
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…
On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
Evan Miller, Tai-Peng Tsai
In this paper, we consider axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. We show that in dimension , axisymmetric, swirl-free sol…
Remarks on local regularity of axisymmetric solutions to the 3D Navier--Stokes equations
Hui Chen, Tai-Peng Tsai, Ting Zhang
In this note, a new local regularity criteria for the axisymmetric solutions to the 3D Navier--Stokes equations is investigated. It is slightly supercritical and implies an upper b…
Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schr{ö}dinger equation
Perla Kfoury, Stefan Le Coz, Tai-Peng Tsai
For the double power one dimensional nonlinear Schr{ö}dinger equation, we establish a complete classification of the stability or instability of standing waves with positive freque…
Finite energy Navier-Stokes flows with unbounded gradients induced by localized flux in the half-space
Kyungkeun Kang, Baishun Lai, Chen-Chih Lai +1
For the Stokes system in the half space, Kang [Math.~Ann.~2005] showed that a solution generated by a compactly supported, Hölder continuous boundary flux may have unbounded normal…
Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
We study the regular sets of local energy solutions to the Navier-Stokes equations in terms of conditions on the initial data. It is shown that if a weighted norm of the init…
Existence and stability of standing waves for one dimensional NLS with triple power nonlinearities
Fei Liu, Tai-Peng Tsai, Ian Zwiers
In this note we study analytically and numerically the existence and stability of standing waves for one dimensional nonlinear Schrödinger equations whose nonlinearities are the su…
On bifurcation of self-similar solutions of the stationary Navier-Stokes equations
Hyunju Kwon, Tai-Peng Tsai
Landau solutions are special solutions to the stationary incompressible Navier-Stokes equations in the three dimensional space excluding the origin. They are self-similar and axisy…
The Green tensor of the nonstationary Stokes system in the half space
Kyungkeun Kang, Baishun Lai, Chen-Chih Lai +1
We prove the first ever pointwise estimates of the (unrestricted) Green tensor and the associated pressure tensor of the nonstationary Stokes system in the half-space, for every sp…
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…
An -regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
We prove an -regularity criterion for the 3D Navier-Stokes equations in terms of initial data. It shows that if a scaled local norm of initial data is sufficiently small a…
Liouville type theorems for stationary Navier-Stokes equations
Tai-Peng Tsai
We show that any smooth stationary solution of the 3D incompressible Navier-Stokes equations in the whole space, the half space, or a periodic slab must vanish under the condition…
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…
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…
Short time regularity of Navier-Stokes flows with locally initial data and applications
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in . The result is applie…
Existence, uniqueness, and regularity results for elliptic equations with drift terms in critical weak spaces
Hyunseok Kim, Tai-Peng Tsai
We consider Dirichlet problems for linear elliptic equations of second order in divergence form on a bounded or exterior smooth domain in , , with drifts…
Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation
Hyunju Kwon, Tai-Peng Tsai
Consider the Cauchy problem of incompressible Navier-Stokes equations in with uniformly locally square integrable initial data. If the square integral of the initial…
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 $\…