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Uniqueness of prescribed-node radial bound states for a zero-mass double-power equation
Wenjing Chen, Zexi Wang
We study radial bound states of \[ Δu-\abs{u}^{q-1}u+\abs{u}^{p-1}u=0 \quad\text{in }\R^n, \qquad n\ge3,\qquad 1<q<p<\frac{n+2}{n-2}. \] For every integer , we prove that th…
Flexibility for the Three-Dimensional Navier-Stokes Equations via Moving Hill Vortices
Quoc-Hung Nguyen, Zexi Wang
We construct weak solutions of the three-dimensional incompressible Navier--Stokes equations on the torus. The convex-integration scheme is based on the moving-dipole construction…
Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group
Wenjing Chen, Zexi Wang
We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group , \begin{equatio…
Remainder terms and sharp quantitative stability for a nonlocal Sobolev inequality on the Heisenberg group
Wenjing Chen, Zexi Wang
In this paper, we study the following nonlocal Sobolev inequality on the Heisenberg group \begin{equation}\label{eq:HLS} S_{HL}(Q,μ) \left(\int_{\mathbb{H}^{n}}\int_{\mathbb{H}^{n}…