For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of with given indata and diffuse reflection on the boundary.
We give the estimate for the Stokes semigroup in a perturbed half-space and some global in time existence theorems for small solutions to the Navier-Stokes equation.
In this paper, we study the nonstationary Stokes equation with Neumann boundary condition in a bounded or an exterior domain in ℝⁿ, which is the linearized model problem of the free boundary value problem. Mainly, we prove estimates for the semigroup of the Stokes operator. Comparing with the non-slip boundary condition case, we have the better decay estimate for the gradient of the semigroup in the exterior domain case because of the null force at the boundary.
We study solutions of the steady Navier-Stokes equations in a bounded 2D domain with the slip boundary conditions admitting flow across the boundary. We show conditions guaranteeing uniqueness of the solution. Next, we examine the structure of the solution considering an approximation given by a natural linearization. Suitable error estimates are also obtained.
A numerical study of a two-dimensional model for premixed gas combustion in a narrow, semi-infinite channel with no-slip boundary condition is performed. The work is motivated by recent theoretical advances revealing the major role of hydraulic resistance in deflagration-to-detonation transition, one of the central yet still inadequately understood phenomena of gaseous combustion. The work is a continuation and extension of recently reported results over non-isothermal boundary conditions, wider...
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in...
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in Lions...