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Construction of solutions for the critical polyharmonic equation with competing potentials
Wenjing Chen, Zexi Wang
In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Δ)^m u+V(|y'|,y'')u=Q(|y'|,y'')u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \mathb…
Blowing-up solutions for the Choquard type Brezis-Nirenberg problem in dimension three
Wenjing Chen, Zexi Wang
In this paper, we are interested in the existence of solutions for the following Choquard type Brezis-Nirenberg problem \begin{align*} \left\{ \begin{array}{ll} -Δu=\displaystyle\B…
New type of solutions for a critical Grushin-type problem with competing potentials
Wenjing Chen, Zexi Wang
In this paper, we consider a critical Grushin-type problem with double potentials. By applying the reduction argument and local Pohouzaev identities, we construct a new family of s…
New type of solutions for the critical polyharmonic equation
Wenjing Chen, Zexi Wang
In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Δ)^m u+V(|y'|,y'')u=u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \mathbb{R}^3\time…
New Regularity Criteria for Navier-Stokes and SQG Equations in Critical Spaces
Yiran Xu, Ly Kim Ha, Haina Li +1
In this paper, we investigate some priori estimates to provide the critical regularity criteria for incompressible Navier-Stokes equations on and super critical surf…