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We prove the global existence of weak solutions to the Navier-Stokes equations for compress-ible, heat-conducting flow in one space dimension with large, discontinuous initial data, and we obtain a-priori estimates for these solutions which are independent of time, sufficient to determine their asymptotic behavior. In particular, we show that, as time goes… (More)

Keywords: Global-in-time existence Large data Large-time behaviour Fluid–particle interaction model Compressible and viscous fluid Smoluchowski equation a b s t r a c t This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid–particle interaction model in the so-called bubbling regime. The mixture occupies the… (More)

We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric flocking potential, the Cucker-Smale equation with additional strong local alignment, and a newly proposed model by Motsch and Tadmor [14]. The main tools… (More)

1. Introduction. 2. Preliminaries and main results. 3. Wave front tracking approximations. 4. The Lyapunov functional. 5. Stability of approximate solutions. 6. Proofs of the main theorems.

We prove the global existence of solutions of the Navier-Stokes equations describing the dynamic combustion of a compressible, exothermically reacting fluid, and we study the large-time behavior of solutions, giving necessary and sufficient conditions for complete combustion in certain cases. The adiabatic constants and specific heats of the burned… (More)

- B. Dacorogna, I. Fonseca, J. Malý, K. Trivisa
- 2003

The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a C

We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the… (More)

Several Glimm-type functionals for (piecewise smooth) approximate solutions of nonlinear hyperbolic systems have been introduced in recent years. In this paper, following a work by Baiti and Bressan on genuinely nonlinear systems we provide a framework to prove that such functionals can be extended to general functions with bounded variation and we… (More)

- Hantaek Bae, Konstantina Trivisa
- 2010

The Doi model for the suspensions of rod-like molecules in a dilute regime describes the interaction between the orientation of rod-like polymer molecules on the microscopic scale and the macroscopic properties of the fluid in which these molecules are contained (cf. Doi and Edwards[11]). The orientation distribution of the rods on the microscopic level is… (More)

The rate of convergence for vanishing viscosity approximations to hyperbolic balance laws is established. The result applies to systems that are strictly hyperbolic and genuinely nonlinear with a source term satisfying a special mechanism that induces dissipation. The proof relies on error estimates that measure the interaction of waves. Shock waves are… (More)