Related papers: Almost Global Existence for 2-D Incompressible Iso…
We identify the wave maps type nonlinearities of incompressible Hookean elastodynamics equations in Lagerangian coordinates, and iterate them in the adapted $U^2$-type spaces to prove the small data global well-posedness in the critical…
Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the balance of momentum and internal energy of a heat-conducting elastic body, preserving the positivity of temperature. So far, no global existence results…
The isotropic Landau (Coulomb) operator was introduced in kinetic theory by Krieger and Strain (Comm. Partial Differential Equations, 2012). In this work, we study the spatially inhomogeneous Vlasov--Poisson--isotropic Landau system. We…
This paper is concerned with a mathematical model which describes 2-D flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain. We prove the existence and uniqueness theorem for global (in time) weak solutions and…
We consider the Cauchy problem in $\mathbb{R}^{n}$ for wave and beam equations with frictional, viscoelastic damping, and a new power nonlinearity. In addition to the solution and its total energy, we define the following quantity:…
In this paper we focus on the Cauchy problem for the incompressible Navier-Stokes equation with a rough external force. If the given rough external force is small, we prove the local-in-time existence of this system for any initial data…
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in Besov spaces. Our estimates generalize the estimates…
We consider the Cauchy problem defined for a general class of nonlocal wave equations modeling bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. We…
We consider the Cauchy problems in the whole space for the wave equation with a weighted L^{1}-initial data. We first derive sharp infinite time blowup estimates of the L^{2}-norm of solutions in the one and two dimensional cases. Then, we…
This present paper is dedicated to the study of the Cauchy problem of the two-dimensional Euler-Boussinesq-B$\rm\acute{e}$nard equations which couple the incompressible Euler equations for the velocity and a transport equation with critical…
The Cauchy problem for the two dimensional compressible Euler equations with data in the Sobolev space $H^s(\mathbb R^2)$ is known to have a unique solution of the same Sobolev class for a short time, and the data-to-solution map is…
In this paper, we study the Cauchy problem for the energy-critical inhomogeneous nonlinear Schr\"{o}dinger equation with inverse-square potential \[iu_{t} +\Delta u-c|x|^{-2}u=\lambda|x|^{-b} |u|^{\sigma } u,\; u(0)=u_{0} \in…
We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an…
In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to…
The global existence of weak solutions of the incompressible viscoelastic flows in two spatial dimensions has been a long standing open problem, and it is studied in this paper. We show the global existence if the initial deformation…
In this article, we will study unbounded solutions of the 2D incompressible Euler equations. One of the motivating factors for this is that the usual functional framework for the Euler equations (e.g. based on finite energy conditions, such…
We study the small data global well-posedness and time-decay rates of solutions to the Cauchy problem for 3D compressible Navier-Stokes-Allen-Cahn equations via a refined pure energy method. In particular, the optimal decay rates of the…
We consider the Cauchy problem for systems of semilinear wave equations in two space dimensions. We present a structural condition on the nonlinearity under which the energy decreases to zero as time tends to infinity if the Cauchy data are…
As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces…
In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases.…