相关论文: Enhanced Dissipation and Global Well-Posedness for…
In this paper, we study the 3-D parabolic-parabolic and parabolic-elliptic Keller-Segel models with Couette flow in $\mathbb{R}^3$. We prove that the blow-up phenomenon of solution can be suppressed by enhanced dissipation of large Couette…
In this paper, we study the three-dimensional non-isentropic compressible fluid-particle flows. The system involves coupling between the Vlasov-Fokker-Planck equation and the non-isentropic compressible Navier-Stokes equations through…
We study the Cauchy problem of three-dimensional compressible non-isentropic magnetohydrodynamic (MHD) fluids with both interior and far field vacuum states. Applying delicate energy estimates, initial layer analysis, and continuation…
The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the…
This paper studies the Cauchy problem for three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic equations with vacuum as far field density. We prove the global existence and uniqueness of strong solutions provided…
We consider the Cauchy problem of the viscous $\beta$-plane equations. We first establish the global well-posedness of the system for the initial data sufficiently small compared to the Rossby parameter. The smoothing effect of the flow is…
We investigate the Cauchy problem of three-dimensional compressible non-isothermal nematic liquid crystal flows in $\mathbb{R}^3$. We derive the global existence and uniqueness of strong solutions with both interior and far field vacuum…
This paper focuses on Cauchy problem for the three-dimensional two-fluid type model, in which the presence of vacuum is permitted. Under some assumptions that the initial data satisfy appropriate regularity conditions and a compatibility…
This paper is devoted to the well-posedness theory of piston problem for compressible {combustion} Euler flows with physical ignition condition. A significant combustion phenomena called detonation will occur provided the reactant is…
We investigate global well-posedness to the Cauchy problem of three-dimensional compressible viscous and heat-conducting micropolar fluid equations with zero density at infinity. By delicate energy estimates, we establish global existence…
In this paper, we establish linear enhanced dissipation results for the three-dimensional Boussinesq equations around a stably stratified Couette flow, in the viscous and thermally diffusive setting. The dissipation rates are faster…
We study the Cauchy problem for the cubic nonlinear Schroedinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
The mathematical analysis on the behavior of the entropy for viscous, compressible, and heat conducting magnetohydrodynamic flows near the vacuum region is a challenging problem as the governing equation for entropy is highly degenerate and…
A theory of flame propagation in curved channels is developed within the framework of the on-shell description of premixed flames. Employing the Green function appropriate to the given channel geometry, an implicit integral representation…
In this paper, we consider the global well-posedness and time-decay rates of solution to the Cauchy problem for 3D convective Cahn-Hilliard equation with double-well potential via a refined pure energy method. In particular, the optimal…
In order to analyze the wave propagation in three-dimensional isotropic and viscoelastic body, the Cauchy initial value problem on unbounded domain is considered for the wave equation written as a system of fractional partial differential…
We study the large-data Cauchy problem for two dimensional Oldroyd model of incompressible viscoelastic fluids. We prove the global-in-time existence of the Leray-Hopf type weak solutions in the physical energy space. Our method relies on a…
The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…
We discuss what is an optimal velocity field for more heat transfer and less energy dissipation under the constraints of the continuity equation for the velocity and the advection-diffusion equation for temperature in plane Couette flow.…