Related papers: Well-posedness for a molecular beam epitaxy model

We consider the Navier-Stokes Cauchy problem with an initial datum in a weighted Lebesgue space. The weight is a radial function increasing at infinity. Our study partially follows the ideas of the paper by G.P. Galdi and P. Maremonti "On…

Reflection high-energy electron diffraction (RHEED) is a ubiquitous in situ molecular beam epitaxial (MBE) characterization tool. Although RHEED can be a powerful means for crystal surface structure determination, it is often used as a…

We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…

We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space under some admissible condition. The result…

The long time behavior of a kind of fully magnetic effected nonlinear piezoelectric beam with viscoelastic infinite memory is considered. The well-posedness of this nonlinear coupled PDEs system is showed by mean of the semigroup theories…

In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity…

For the past two decades the Villain-Lai-Das Sarma equation has served as the theoretical framework for conserved surface growth processes, such as molecular-beam epitaxy. However some phenomena, such as mounding, are yet to be fully…

The Cauchy problem of a multi-dimensional ($d\geqslant 2$) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close…

We study the Cauchy problem in $n$-dimensional space for the system of Navier-Stokes equations in critical mixed-norm Lebesgue spaces. Local well-posedness and global well-posedness of solutions are established in the class of critical…

I propose to use laser heating both for the substrate and the thermal evaporation sources in a vacuum chamber operating at pressures from XHV to values where the mean free path of the particles approaches or slightly exceeds the…

We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…

Atomically sharp epitaxial growth of Bi2Se3 films is achieved on Si (111) substrate with MBE (Molecular Beam Epitaxy). Two-step growth process is found to be a key to achieve interfacial-layer-free epitaxial Bi2Se3 films on Si substrates.…

We establish the existence of global weak solution in 2D and 3D, as well as the uniqueness of weak solution in 2D, for the Darcy-Boussinesq model for convection in layered porous media with square integrable initial data. We also derived…

We observe a catalytic mechanism during the growth of III-O and IV-O materials by suboxide molecular-beam epitaxy ($S$-MBE). By supplying the molecular catalysts In$_2$O and SnO we increase the growth rates of Ga$_2$O$_3$ and In$_2$O$_3$.…

In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for a two-species chemotaxis consumption model in a bounded smooth but not necessarily convex domain $\Omega\subset \mathbb{R}^n…

Interests in two-dimensional transition-metal dichalcogenides have prompted some recent efforts to grow ultrathin layers of these materials epitaxially using molecular-beam epitaxy. However, growths of monolayer and bilayer WSe2, an…

We study global well-posedness of strong solutions for the nonhomogeneous Navier-Stokes equations with density-dependent viscosity and initial density allowing vanish in $\mathbb{R}^2$. Applying a logarithmic interpolation inequality and…

We study the Cauchy problem for the chemotaxis Navier-Stokes equations and the Keller-Segel-Navier-Stokes system. Local-in-time and global-in-time solutions satisfying fundamental properties such as mass conservation and nonnegativity…

We study the chemical ordering in Bi$_2$Te$_{3-x}$Se$_x$ grown by molecular beam epitaxy on Si substrates. We produce films in the full composition range from x = 0 to 3, and determine their material properties using energy dispersive X-ray…

In this paper we study the Cauchy problem for one multidimensional compressible nonlocal model of the dissipative quasi-geostrophic equations. First, we obtain the local existence and uniqueness of the smooth non-negative solution or the…