Marcelo Martins dos Santos

• Abstract

  1 )Research: during the three months research stay at IMECC, Prof. Vladimir will work on research in order to develop a mathematical theory of micropolar viscoplastic fluids. It is a challenge to prove a global existence theorem. In contrast to Navier-Stokes equations, the constitutive laws are not regular. This is why a free boundary arises which divides a fluid and a rigid (plug) zones.…

  Equations of micropolar viscoplastic fluids, AV.EXT
• Dynamics of singularity manifolds for compressible, viscous., AR.EXT
• Grzegorz Lukaszewicz | Warsaw University - Polônia, AV.EXT

(Only some records are available in English at this moment)

• Abstract

  Our research project is centered on mathematical formalisms of fluid mechanics. Particularly, we aim to show how the Reynolds Transport Theorem applied for momentum conservation yields the Cauchy equation. Furthermore, we will try to use physical principles to infer the form of the stress tensor for Newtonian fluids. The stress tensor associated with the Cauchy equation will be rearranged…

  Basic Mathematical fluid dynamics, BP.IC

• Abstract

  The main goal of the project is to continue the investigation of the theory of "averaging lemmas" and apply it to concrete problems involving degenerate parabolic-hyperbolic equations. More specifically, for these equations, it is intended to study an initial value problem for a stochastic version with periodic boundary conditions, to investigate Sobolev's regularity of entropy and kineti…

  Degenerate parabolic-hyperbolic equations and averaging lemmas, BP.PD

• Abstract

  In this proposal we intend to investigate specific conditions to guarantee existence and uniqueness of delta shock wave for the Riemann problem associated to some general 2x2 systems of conservation laws in regions where do not existclassical solutions, to obtain (to proof) some theorem in this regard an write a paper in order to submit for publication in a good international journal. (AU)

  Delta shock waves for some general 2x2 system of conservation laws, BP.PD

(Only some records are available in English at this moment)

• Abstract

  We consider the Navier-Stokes equations for compressible fluids with viscosity. Our goal is to show the existence of a solution in the presence of vacuum. We intend to solve the problem in dimension two. The three dimension case will be consider depending on the difficulty of the problem. We will assume that initially the vacuum is located outside the exterior of a bounded domain which bo…

  Free boundary 2D compressible Navier-Stokes equations, BE.PQ