27 citations · 50 across the 17 of their papers we have counts for
17 papers
The optimal time-decay estimates for 2-D inhomogeneous Navier-Stokes equations
Yanlin Liu
In this paper, we derive the optimal time-decay estimates for 2-D inhomogeneous Navier-Stokes equations. In particular, we prove that $\|u(t)\|_{\dot{B}^θ_{p,1}({\mathop{\mathbb R\…
Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain
Ning Liu, Yanlin Liu, Ping Zhang
In this paper, we first establish the global existence and stability of solutions to 3-D classical Navier-Stokes equations in an infinite cylindrical domain with large Fouri…
On the one time-varying component regularity criteria for 3-D Navier-Stokes equations
Yanlin Liu, Ping Zhang
In this paper, we consider the one time-varying component regularity criteria for local strong solution of 3-D Navier-Stokes equations. Precisely, if is a piecewise un…
On the global stability of large Fourier mode for 3-D Navier-Stokes equations
Yanlin Liu, Ping Zhang
In this paper, we first prove the global existence of strong solutions to 3-D incompressible Navier-Stokes equations with solenoidal initial data, which writes in the cylindrical c…
On the existence and structures of almost axisymmetric solutions to 3-D Navier-Stokes equations
Yanlin Liu, Li Xu
In this paper, we consider 3-D Navier-Stokes equations with almost axisymmetric initial data, which means that by writing in the cylindrical co…
The influence of viscous coefficients on the lifespan of 3-D anisotropic Navier-Stokes system
Tiantian Hao, Yanlin Liu
The anisotropic Navier-Stokes system arises in geophysical fluid dynamics, which is derived by changing $-ν\D$ in the classical Navier-Stokes system to $-(ν_1\partial^2_1+ν_2\parti…
Long-time asymptotics of -D axisymmetric Navier-Stokes equations in critical spaces
Yanlin Liu
We show that any unique global solution (here we do not require any smallness condition beforehand) to 3-D axisymmetric Navier-Stokes equations in some scaling invariant spaces mus…
Relative Equivariant Coarse Index Theorem and Relative -Index Theorem
Xiaoman Chen, Yanlin Liu, Dapeng Zhou
In this paper, we give a definition of the relative equivariant coarse index for proper actions and derive a relative equivariant coarse index theorem connecting this index with th…
Global well-posedness of -D anisotropic Navier-Stokes system with small unidirectional derivative
Yanlin Liu, Marius Paicu, Ping Zhang
In \cite{LZ4}, the authors proved that as long as the one-directional derivative of the initial velocity is sufficiently small in some scaling invariant spaces, then the classical…
Global solutions of -D Navier-Stokes system with small unidirectional derivative
Yanlin Liu, Ping Zhang
Given initial data $u_0=(u_0^\h,u_0^3)\in H^{-\d,0}\cap H^{\f12}(\R^3)$ with both~$\uh_0$ and~$\nabla_{\rm h}\uh_0$ belonging to ~$L^2(\R^3)\cap L^\infty(\R_\v;L^2(\R^2_\h))$ and $…
Uniqueness of axisymmetric viscous flows originating from positive linear combinations of circular vortex filaments
Guillaume Lévy, Yanlin Liu
Following the recent papers [9] and [10] by T. Gallay and V. uSverák, in the line of work initiated by H. Feng and V. uSverák in their paper [3], we prove the uniqueness of a solut…
Critical one component anisotropic regularity for 3-D Navier-Stokes system
Yanlin Liu, Ping Zhang
Let us consider an initial data for the classical 3D Navier-Stokes equation with vorticity belonging to . We prove that if the solution associated with…
Global well-posedness of 3-D anisotropic Navier-Stokes system with large vertical viscous coefficient
Yanlin Liu, Ping Zhang
In this paper, we first prove the global well-posedness of 3-D anisotropic Navier-Stokes system provided that the vertical viscous coefficient of the system is sufficiently large c…
On the global well-posedness of 3D axisymmetric MHD system with pure swirl magnetic field
Yanlin Liu
In this paper, we consider the axisymmetric MHD system with nearly critical initial data having the special structure: $u_0=u_0^r e_r+\ut_0 e_θ+u_0^z e_z, ~b_0=b_0^θe_θ.$ We prove…
On the global well-posedness of 3-D axi-symmetric Navier-Stokes system with small swirl component
Yanlin Liu, Ping Zhang
In this paper, we prove the local well-posedness of 3-D axi-symmetric Navier-Stokes system with initial data in the critical Lebesgue spaces. We also obtain the global well-posedne…
Global regularity of three dimensional density patch for inhomogeneous incompressible viscous flow
Xian Liao, Yanlin Liu
The present work is devoted to proving that the boundary regularity of the three dimensional density patch persists by time evolution for inhomogeneous incompressible viscous flow,…
On the critical one-component velocity regularity criteria to 3-D incompressible MHD system
Yanlin Liu
Let be a smooth enough solution of 3-D incompressible MHD system. We prove that if blows up at a finite time , then for any , there holds $\int…