In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip domain.We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit ...In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip domain.We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.展开更多
This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribe...This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given.展开更多
This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a ...This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.展开更多
The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ d...The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.展开更多
文摘In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip domain.We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.
基金Project supported by the European Research and Training Network "HMS 2000" of the European Union under Contract HPRN-2000-00109.
文摘This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given.
文摘This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region,China(Nos.9041637,CiyuU100711)
文摘The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω R^n→ E^n with prescribed metric tensor field(g ij) : Ω→ S^n>, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.
