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Global solutions to the micropolar compressible flow with constant coefficients and vacuum
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Ling Wan, Lan ZhangAbstractWe prove the global existence and uniqueness of strong solutions for an initial boundary value problem modeling the motion of the compressible micropolar fluids in one dimensional space. Compared with former studies, we are concerned with the nonisentropic case with constant transport coefficients and the initial density is allowed to have vacuum. Our analysis is based on the nonlinear energy method and the crucial step is to derive the uniform upper and lower bounds on the ratio of the density...
Source: Nonlinear Analysis: Real World Applications - August 30, 2019 Category: Research Source Type: research

Optimal distributed control of a 2D simplified Ericksen–Leslie system for the nematic liquid crystal flows
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Qiao LiuAbstractWe study the initial boundary value problem of a simplified Ericksen–Leslie system modeling the incompressible nematic liquid crystal flows in two dimensions of space, where the equations of the velocity field are characterized by a time-dependent external force g(t) and a no-slip boundary condition, and the equations for the molecular orientation are subjected to a time-dependent Dirichlet boundary condition h(t). Based on the recently addressed well-posedness and regularity results of the system, we p...
Source: Nonlinear Analysis: Real World Applications - August 29, 2019 Category: Research Source Type: research

Steady vortex patch with polygonal symmetry for the planar Euler equations in a disc
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Daomin Cao, Jie Wan, Guodong WangAbstractIn this paper, we construct two types of vortex patch equilibria for the two-dimensional Euler equations in a disc. The first type is called the “N+1 type” equilibrium, in which a central vortex patch is surrounded by N identical patches with opposite signs, and the other type is called the “2N type” equilibrium, in which the centers of N identical positive patches and N negative patches lie evenly on a circle. The construction is performed by solving a variational problem...
Source: Nonlinear Analysis: Real World Applications - August 29, 2019 Category: Research Source Type: research

Existence and uniqueness of solution for two one-phase Stefan problems with variable thermal coefficients
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Julieta Bollati, María F. Natale, José A. Semitiel, Domingo A. TarziaAbstractOne dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet, a Neumann or a Robin type condition at fixed face x=0. Moreover, it is proved that the solution of the problem with the Robin type condition converges to the solution of the problem with the Dirichlet condition at the fixed face. Computational exampl...
Source: Nonlinear Analysis: Real World Applications - August 23, 2019 Category: Research Source Type: research

Nonlinear oscillations in the modified Leslie–Gower model
Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Jaume Giné, Claudia VallsAbstractIn this paper we study the existence of nonlinear oscillations of a modified Leslie–Gower model around the positive equilibrium point. It is proved that at least one limit cycle can exist bifurcating from it but that this point is never a center, that is, there does not exist an infinite number of nonlinear oscillations around it. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - August 23, 2019 Category: Research Source Type: research