相关论文: Strong Time-Periodic Solutions to the 3D Primitive…
We prove the existence of time periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces. We consider the cubic Ginzburg-Landau equation with an external force $g$ satisfying the oddness condition $g(-x,t)=-g(x,t)$.…
In this paper, we consider the initial boundary value problem for the three-dimensional viscous primitive equations of large-scale moist atmosphere which are used to describe the turbulent behavior of long-term weather prediction and…
This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…
In this paper we consider the (simplified) 3-dimensional primitive equations with \emph{physical boundary conditions}. We show that the equations with constant forcing have a bounded absorbing ball in the $H^1$-norm and that a solution to…
Criteria for the existence of $T$-periodic solutions of nonautonomous parabolic equation $u_t = \Delta u + f(t,x,u)$, $x\in\mathbb{R}^N$, $t>0$ with asymptotically linear $f$ will be provided. It is expressed in terms of time average…
This work is devoted to the analysis of strong solutions to the Abels-Garcke-Gr\"{u}n (AGG) model in three dimensions. First, we prove the existence of local-in-time strong solutions originating from an initial datum $(\mathbf{u}_0,…
In this paper, we consider the initial-boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation. Global well-posedness of strong solutions are…
Consider the bidomain equations subject to ionic transport described by the models of FitzHugh-Nagumo, Aliev-Panfilov, or Rogers-McCulloch. It is proved that this set of equations admits a unique, strong T-periodic solution provided it is…
This paper deals with the Vlasov-Stokes' system in three dimensions with periodic boundary conditions in the spatial variable. We prove the existence of a unique strong solution to this two-phase model under the assumption that initial…
For the stochastic Navier-Stokes equations with a multiplicative white noise on ${\mathbb T}^{3}$, we prove that there exists a unique strong solution locally in time when the initial datum belongs to $L^p(\Omega; L^p)$ for $p>3$.
This paper concerns the large-time behavior of perturbations around a time-periodic solution to the Navier-Stokes-Fourier system in the three-dimensional whole space. The time-periodic solution exists when a given external force is small…
The concept of a fundamental solution to the time-periodic Stokes equations in dimension $n\geq 2$ is introduced. A fundamental solution is then identified and analyzed. Integrability and pointwise estimates are established.
We prove the existence of strong solutions to Navier-Stokes equations in three dimensional thin domains. Our proof is based on the energy and the Poincar\'e inequalities as well as contraction principle argument and is free of the mean…
Consider the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, and subject to outer forces. It is shown that this set of equations is globally strongly well-posed…
Under the assumption that the infinite product of evolution process converges almost surely, the set of strong solutions are characterized by a compact space, which may be regarded as the set of possible initial states.
We construct time almost-periodic solutions (global in time) with finite regularity to the incompressible Euler equations on the torus $\T^d$, with $d=3$ and $d\in\N$ even.
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain $\Omega $ can be extended, under suitable conditions, to the case in which the…
We consider a Kepler problem in dimension two or three, with a time-dependent $T$-periodic perturbation. We prove that for any prescribed positive integer $N$, there exist at least $N$ periodic solutions (with period $T$) as long as the…
Consider a difference equation which takes the k-th largest output of m functions of the previous m terms of the sequence. If the functions are also allowed to change periodically as the difference equation evolves this is analogous to a…
In this article, an $L^p$-approach to the primitive equations is developed. In particular, it is shown that the three dimensional primitive equations admit a unique, global strong solution for all initial data $a \in [X_p,D(A_p)]_{1/p}$…