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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 $…
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…
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…