110 citations · 420 across the 33 of their papers we have counts for
35 papers
Global well-posedness of strong solutions to a model for the morning glory cloud
Jinkai Li, Yuan Ma, Dong Wang
In this paper, we investigate the global well-posedness of strong solution to a model recently derived by Constantin-Johnson \cite{CaJo} which describes the nonlinear wave propagat…
Local well-posedness of strong solutions to the non-isentropic compressible primitive equations with vertical diffusion
Rupert Klein, Jinkai Li, Xin Liu +1
Due to the absence of dynamical equation in the vertical momentum component of the primitive equations (PEs) of atmospheric dynamics, the vertical component of the velocity can be…
Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity II: close to initial data
Chongsheng Cao, Jinkai Li, Edriss S. Titi +1
In this paper, we consider the initial-boundary value problem to the three-dimensional primitive equations for the oceanic and atmospheric dynamics with only horizontal eddy viscos…
Entropy-bounded solutions to the Cauchy problem of compressible planar non-resistive magnetohydrodynamics equations with far field vacuum
Jinkai Li, Mingjie Li, Yang Liu +1
We investigate the Cauchy problem to the compressible planar non-resistive magnetohydrodynamic equations with zero heat conduction. The global existence of strong solutions to such…
Instantaneous unboundedness of the entropy and uniform positivity of the temperature for the compressible Navier-Stokes equations with fast decay density
Jinkai Li, Zhouping Xin
This paper concerns the physical behaviors of any solutions to the one dimensional compressible Navier-Stokes equations for viscous and heat conductive gases with constant viscosit…
Global well-posedness for the thermodynamically refined passively transported nonlinear moisture dynamics with phase changes
Sabine Hittmeir, Rupert Klein, Jinkai Li +1
In this work we study the global solvability of moisture dynamics with phase changes for warm clouds. We thereby in comparison to previous studies [Hittmeir-Klein-Li-Titi (2017)] t…
Global small solutions to heat conductive compressible nematic liquid crystal system: smallness on a scaling invariant quantity
Jinkai Li, Qiang Tao
In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fiel…
Propagation of uniform boundedness of entropy and inhomogeneous regularities for viscous and heat conductive gases with far field vacuum in three dimensions
Jinkai Li, Zhouping Xin
Due to the highly degeneracy and singularities of the entropy equation, the physical entropy for viscous and heat conductive polytropic gases behave singularly in the presence of v…
Local existence and uniqueness of heat conductive compressible Navier-Stokes equations in the presence of vacuum and without initial compatibility conditions
Jinkai Li, Yasi Zheng
In this paper, we investigate the initial-boundary value problem to the heat conductive compressible Navier-Stokes equations. Local existence and uniqueness of strong solutions is…
Global well-posedness of -weak solutions to the primitive equations without vertical diffusivity
Jinkai Li, Guozhi Yuan
In this paper, we consider the initial boundary value problem in a cylindrical domain to the three dimensional primitive equations with full eddy viscosity in the momentum equation…
The primitive equations approximation of the anisotropic horizontally viscous Navier-Stokes equations
Jinkai Li, Edriss S. Titi, Guozhi Yuan
In this paper, we provide rigorous justification of the hydrostatic approximation and the derivation of primitive equations as the small aspect ratio limit of the incompressible th…
Global Well-posedness for the Primitive Equations Coupled to Nonlinear Moisture Dynamics with Phase Changes
Sabine Hittmeir, Rupert Klein, Jinkai Li +1
In this work we study the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present i…
The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation
Jinkai Li, Edriss S. Titi
An important feature of the planetary oceanic dynamics is that the aspect ratio (the ratio of the depth to horizontal width) is very small. As a result, the hydrostatic approximati…
Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity
Chongsheng Cao, Jinkai Li, Edriss S. Titi
In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertic…
Nonuniqueness of nematic liquid crystal flows in dimension three
Huajun Gong, Tao Huang, Jinkai Li
For suitable initial and boundary data, we construct infinitely many weak solutions to the nematic liquid crystal flows in dimension three. These solutions are in the axisymmetric…
Global well-posedness for passively transported nonlinear moisture dynamics with phase changes
Sabine Hittmeir, Rupert Klein, Jinkai Li +1
We study a moisture model for warm clouds that has been used by Klein and Majda as a basis for multiscale asymptotic expansions for deep convective phenomena. These moisture balanc…
Strong solutions to the 3D primitive equations with only horizontal dissipation: near initial data
Chongsheng Cao, Jinkai Li, Edriss S. Titi
In this paper, we consider the initial-boundary value problem of the three-dimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and h…
Local existence and uniqueness of strong solutions to the Navier-Stokes equations with nonnegative density
Jinkai Li
In this paper, we consider the initial-boundary value problem to the nonhomogeneous incompressible Navier-Stokes equations. Local strong solutions are established, for any initial…
Recent Advances Concerning Certain Class of Geophysical Flows
Jinkai Li, Edriss S. Titi
This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dy…
Local well-posedness of strong solutions to density-dependent liquid crystal system
Huajun Gong, Jinkai Li, Chen Xu
In this paper, we study the Cauchy problem to the density-dependent liquid crystal system in . We establish the local existence and uniqueness of strong solutions to t…
Existence and uniqueness of weak solutions to viscous primitive equations for certain class of discontinuous initial data
Jinkai Li, Edriss S. Titi
We establish some conditional uniqueness of weak solutions to the viscous primitive equations, and as an application, we prove the global existence and uniqueness of weak solutions…
A Tropical Atmosphere Model with Moisture: Global Well-posedness and Relaxation Limit
Jinkai Li, Edriss S. Titi
In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture; that was derived in [F…
Global well-posedness of strong solutions to a tropical climate model
Jinkai Li, Edriss S. Titi
In this paper, we consider the Cauchy problem to the TROPIC CLIMATE MODEL derived by Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the bar…
Global well-posedness of the 2D Boussinesq equations with vertical dissipation
Jinkai Li, Edriss S. Titi
We prove the global well-posedness of the two-dimensional Boussinesq equations with only vertical dissipation. The initial data are required to be only in the space $X=…