Mathematical aspects of incompressible fluid dynamics

• Grant number: 07/51490-7
• Support Opportunities: Research Projects - Thematic Grants
• Start date: October 01, 2007
• End date: September 30, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Agreement: CNRS
• Principal Investigator: Milton da Costa Lopes Filho
• Grantee: Milton da Costa Lopes Filho
• Principal researcher abroad: Dragos Iftimie
• Institution abroad: Université Claude Bernard Lyon 1, France
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Pesquisadores principais: Helena Judith Nussenzveig Lopes
• Associated research grant(s): 10/17929-4 - Visit of Evelyne Miot to UNICAMP, AV.EXT; 09/15045-4 - Non-Newtonian flows around small obstacles, AV.EXT
• Associated scholarship(s): 10/11176-4 - The viscous vortex-wave system., BP.PD; 08/09473-0 - Boundary layers in incompressible flows, BP.PD

Abstract

The main objects of this project are solutions of the incompressible flow equations, especially those with irregular or turbulent behavior. Broadly speaking, our research is characterized by the use of the tools of modern analysis in physically relevant problems in fluid dynamics. The ultimate goal of this research is to determine the limits of validity of the classical equations of Euler and Navier-Stokes as models for singular or turbulent flow. Among the specific lines of investigation which we intend to pursue we highlight: 1) flows in singularly perturbed do mains; 2) nonlinear stability of travelling waves associated with ideal flows; 3) singular solutions of the semigeostrophic equations; 4) analytical behavior of boundary layers; 5) flows with concentrated or oscillatory forcing. (AU)

Scientific publications

(28)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DA MOTA, J. C.; SANTOS, M. M.. An application of the monotone iterative method to a combustion problem in porous media. Nonlinear Analysis: Real World Applications, v. 12, n. 2, p. 1192-1201, APR 2011. (07/51490-7)

BARDOS, C.; LOPES FILHO, M. C.; NIU, DONGJUAN; NUSSENZVEIG LOPES, H. J.; TITI, E. S.. STABILITY OF TWO-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS UNDER THREE-DIMENSIONAL PERTURBATIONS AND INVISCID SYMMETRY BREAKING. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 45, n. 3, p. 1871-1885, 2013. (07/51490-7)

AMROUCHE, CHERIF; NGUYEN, HUY HOANG. ELLIPTIC PROBLEMS WITH L-1-DATA IN THE HALF-SPACE. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, v. 5, n. 3, p. 369-397, JUN 2012. (07/51490-7)

BRONZI, ANNE C.; LOPES FILHO, MILTON C.; NUSSENZVEIG LOPES, HELENA J.. WILD SOLUTIONS FOR 2D INCOMPRESSIBLE IDEAL FLOW WITH PASSIVE TRACER. COMMUNICATIONS IN MATHEMATICAL SCIENCES, v. 13, n. 5, p. 1333-1343, 2015. (07/51490-7)

BRONZI, A. C.; LOPES FILHO, M. C.; NUSSENZVEIG LOPES, H. J.. Global Existence of a Weak Solution of the Incompressible Euler Equations with Helical Symmetry and L-p Vorticity. Indiana University Mathematics Journal, v. 64, n. 1, p. 309-341, 2015. (07/51490-7)

AMBROSE, DAVID M.; LOPES FILHO, MILTON C.; NUSSENZVEIG LOPES, HELENA J.; STRAUSS, WALTER A.. Transport of interfaces with surface tension by 2D viscous flows. INTERFACES AND FREE BOUNDARIES, v. 12, n. 1, p. 23-44, 2010. (07/51490-7)

KELLIHER, JAMES P.; LOPES FILHO, MILTON C.; NUSSENZVEIG LOPES, HELENA J.. Vanishing viscosity limit for an expanding domain in space. ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE, v. 26, n. 6, p. 2521-2537, NOV-DEC 2009. (07/51490-7, 07/03713-7)

FARIA, JOSIANE C. O.; LOPES FILHO, MILTON C.; NUSSENZVEIG LOPES, HELENA J.. Weak stability of Lagrangian solutions to the semigeostrophic equations. Nonlinearity, v. 22, n. 10, p. 2521-2539, OCT 2009. (07/51490-7)

BUSUIOC, A. V.; IFTIMIE, D.; LOPES FILHO, M. C.; LOPES, H. J. NUSSENZVEIG. Incompressible Euler as a limit of complex fluid models with Navier boundary conditions. Journal of Differential Equations, v. 252, n. 1, p. 624-640, JAN 1 2012. (07/51490-7)

LOPES FILHO, MILTON C.; MIOT, EVELYNE; NUSSENZVEIG LOPES, HELENA J.. Existence of a Weak Solution in L (p) to the Vortex-Wave System. JOURNAL OF NONLINEAR SCIENCE, v. 21, n. 5, p. 685-703, OCT 2011. (07/51490-7)

LOPES FILHO, MILTON C.; NUSSENZVEIG LOPES, HELENA J.; PRECIOSO, JULIANA C.. LEAST ACTION PRINCIPLE AND THE INCOMPRESSIBLE EULER EQUATIONS WITH VARIABLE DENSITY. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 363, n. 5, p. 2641-2661, MAY 2011. (07/51490-7)

AMROUCHE, CHERIF; NGUYEN, HUY HOANG. New estimates for the div, curl, grad operators and elliptic problems with L-1-data in the half-space. Applied Mathematics Letters, v. 24, n. 5, p. 697-702, MAY 2011. (07/51490-7)

IFTIMIE, DRAGOS; LOPES FILHO, MILTON C.; NUSSENZVEIG LOPES, HELENA J.. Incompressible Flow Around a Small Obstacle and the Vanishing Viscosity Limit. Communications in Mathematical Physics, v. 287, n. 1, p. 99-115, APR 2009. (07/51490-7, 06/04861-7)

PLANAS, GABRIELA; SUEUR, FRANCK. On the ``viscous incompressible fluid plus rigid body{''} system with Navier conditions. ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE, v. 31, n. 1, p. 55-80, JAN-FEB 2014. (07/51490-7)

IFTIMIE, D.; LOPES FILHO, M. C.; NUSSENZVEIG LOPES, H. J.. Weak vorticity formulation of the incompressible 2D Euler equations in bounded domains. Communications in Partial Differential Equations, v. 45, n. 2, p. 109-145, FEB 1 2020. (07/51490-7)

LOPES FILHO, MILTON C.; NGUYEN, HUY HOANG; LOPES, HELENA J. NUSSENZVEIG. INCOMPRESSIBLE AND IDEAL 2D FLOW AROUND A SMALL OBSTACLE WITH CONSTANT VELOCITY AT INFINITY. QUARTERLY OF APPLIED MATHEMATICS, v. 71, n. 4, p. 679-687, 2013. (07/51490-7)

NICHE, CESAR J.; PLANAS, GABRIELA. Existence and decay of solutions to the dissipative quasi-geostrophic equation with delays. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 75, n. 9, p. 3936-3950, JUN 2012. (07/51490-7)

BURTON, GEOFFREY R.; NUSSENZVEIG LOPES, HELENA J.; LOPES FILHO, MILTON C.. Nonlinear Stability for Steady Vortex Pairs. Communications in Mathematical Physics, v. 324, n. 2, p. 445-463, DEC 2013. (06/51079-2, 07/51490-7)

GUZZO, SANDRO M.; PLANAS, GABRIELA. ON A CLASS OF THREE DIMENSIONAL NAVIER-STOKES EQUATIONS WITH BOUNDED DELAY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 16, n. 1, p. 225-238, JUL 2011. (07/51490-7)

PRECIOSO, JULIANA CONCEICAO. On the regularity of the pressure field of relaxed solutions to Euler equations with variable density. Journal of Mathematical Analysis and Applications, v. 409, n. 1, p. 282-287, JAN 1 2014. (07/51490-7)

FERREIRA, LUCAS C. F.; PLANAS, GABRIELA; VILLAMIZAR-ROA, ELDER J.. ON THE NONHOMOGENEOUS NAVIER-STOKES SYSTEM WITH NAVIER FRICTION BOUNDARY CONDITIONS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 45, n. 4, p. 2576-2595, 2013. (07/51490-7)

GUILLEN-GONZALEZ, FRANCISCO; PLANAS, GABRIELA. On the asymptotic behaviour of the 2D Navier-Stokes equations with Navier friction conditions towards Euler equations. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, v. 89, n. 10, p. 810-822, OCT 2009. (07/51490-7)

FERREIRA, LUCAS C. F.; PRECIOSO, JULIANA C.. Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data. Nonlinearity, v. 24, n. 5, p. 1433-1449, MAY 2011. (07/51490-7)

AMROUCHE, CHERIF; NGUYEN, HUY HOANG. New estimates for the div-curl-grad operators and elliptic problems with L-1-data in the whole space and in the half-space. Journal of Differential Equations, v. 250, n. 7, p. 3150-3195, APR 1 2011. (07/51490-7)

JULIANA CONCEIÇÃO PRECIOSO. A Family of Stationary Solutions to the Euler Equations and Generalized Solutions. Cubo, v. 12, n. 3, p. 13-32, 2010-00-00. (07/51490-7)

NICHE, CESAR J.; PLANAS, GABRIELA. Existence and decay of solutions in full space to Navier-Stokes equations with delays. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 74, n. 1, p. 244-256, JAN 1 2011. (07/51490-7)

PLANAS, GABRIELA; SUEUR, FRANCK. On the "viscous incompressible fluid plus rigid body" system with Navier conditions. ANNALES DE L' INSTITUT HENRI POINCARÉ-ANALYSE NON LINÉAIRE, v. 31, n. 1, p. 26-pg., 2014-01-01. (07/51490-7)

DA MOTA, J. C.; SANTOS, M. M.. An application of the monotone iterative method to a combustion problem in porous media. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 12, n. 2, p. 10-pg., 2011-04-01. (07/51490-7)