The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform
Olivier Glass - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Stabilizability by Stationary Feedback of the Two-Dimensional Euler Equation: The Multiconnected Case
SIAM Journal on Control and Optimization, 2005Co-Authors: Olivier GlassAbstract:We construct a feedback law which allows us to asymptotically stabilize the Euler system for Incompressible Inviscid Fluids in two dimensions, in the case of a multiconnected bounded domain, by means of a control localized on a part of the boundary that meets every connected component of the boundary. This generalizes a result of Coron [{SIAM J. Control Optim., 37 (1999), pp. 1874--1896] concerning simply connected domains.
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an addendum to a j m coron theorem concerning the controllability of the euler system for 2d Incompressible Inviscid Fluids
Journal de Mathématiques Pures et Appliquées, 2001Co-Authors: Olivier GlassAbstract:J.-M. Coron established a result of approximate controllability of the 2D Euler system for Incompressible Inviscid Fluids in the Lp spaces for p<+∞. When the controlled part of the boundary does not meet every connected component of the boundary of the domain, one cannot in general extend the result to the L∞ controllability, because the Kelvin law guarantees some invariants during the process. Here we prove that these invariants are the only objection for the W1,p controllability. Under supplementary natural assumption on the flows we want to connect, we can improve the result to the W2,p approximate controllability.
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An addendum to a J.M. Coron theorem concerning the controllability of the Euler system for 2D Incompressible Inviscid Fluids
Journal de Mathématiques Pures et Appliquées, 2001Co-Authors: Olivier GlassAbstract:J.-M. Coron established a result of approximate controllability of the 2D Euler system for Incompressible Inviscid Fluids in the Lp spaces for p
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exact boundary controllability of 3 d euler equation
ESAIM: Control Optimisation and Calculus of Variations, 2000Co-Authors: Olivier GlassAbstract:We prove the exact boundary controllability of the 3-D Euler equation of Incompressible Inviscid Fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.
Jean-claude Zambrini - One of the best experts on this subject based on the ideXlab platform.
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An entropic interpolation problem for Incompressible viscid Fluids
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2020Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscous Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general form of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its relation with viscous fluid dynamics is discussed.
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An entropic interpolation problem for Incompressible viscid Fluids
Annales de l'Institut Henri Poincaré. Section B. Calculs des Probabilités et Statistiques, 2020Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscid Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general shape of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its connection with the Navier-Stokes equation is established.
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AN ENTROPIC INTERPOLATION PROBLEM FOR Incompressible VISCOUS Fluids
2019Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscous Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general form of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its relation with viscous fluid dynamics is discussed.
Marc Arnaudon - One of the best experts on this subject based on the ideXlab platform.
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An entropic interpolation problem for Incompressible viscid Fluids
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2020Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscous Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general form of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its relation with viscous fluid dynamics is discussed.
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An entropic interpolation problem for Incompressible viscid Fluids
Annales de l'Institut Henri Poincaré. Section B. Calculs des Probabilités et Statistiques, 2020Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscid Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general shape of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its connection with the Navier-Stokes equation is established.
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AN ENTROPIC INTERPOLATION PROBLEM FOR Incompressible VISCOUS Fluids
2019Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscous Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general form of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its relation with viscous fluid dynamics is discussed.
Yongfu Wang - One of the best experts on this subject based on the ideXlab platform.
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two phase Fluids in collision of Incompressible Inviscid Fluids effluxing from two nozzles
Journal of Differential Equations, 2019Co-Authors: Yongfu Wang, Wei XiangAbstract:Abstract This paper is devoted to the mathematical theory of two-dimensional injection of Incompressible, irrotational, and Inviscid Fluids issuing from two infinitely long nozzles into a free stream. In general, there is a free interface with constant jump of the Bernoulli constant on it, which is different and more difficult than the previous related works. Physically, it is called the collision fluid. The main result in this paper is that for given two co-axis symmetric infinitely long nozzles, imposing the incoming mass fluxes in the two nozzles, there exists a unique piecewise smooth collision fluid, such that the free interface of the collision fluid is a C 1 curve, and the pressure is continuous across the interface. As byproducts, the asymptotic behaviors, the positivity of the vertical velocity, monotone relationship between the location of the interface and the incoming mass fluxes are also established.
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Collision of Incompressible Inviscid Fluids effluxing from two nozzles
Calculus of Variations and Partial Differential Equations, 2017Co-Authors: Yongfu WangAbstract:This paper concerns the mathematical theory of the collision problem of two-dimensional Incompressible Inviscid Fluids issuing from two given nozzles. The main result reads that for given two co-axis symmetric semi-infinitely long nozzles with arbitrary variable sections, imposing the incoming mass fluxes in two nozzles, there exists a smooth impinging outgoing jet, such that the two free boundaries of the impinging jet initiate smoothly at the endpoints of the nozzles and approach to some asymptotic direction in downstream, and the pressure on the free surface remains a constant. Furthermore, we show that there exists a unique smooth surface separating the two nonmiscible Fluids and there exists a unique stagnation point in the fluid region and its closure. Moreover, some results on the uniqueness and the estimates of the location of the impinging outgoing jet are also established. Finally, the asymptotic behaviors, the precise estimate to the deflection angle and other properties to the impinging outgoing jet are also considered.
Ana Bela Cruzeiro - One of the best experts on this subject based on the ideXlab platform.
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An entropic interpolation problem for Incompressible viscid Fluids
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2020Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscous Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general form of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its relation with viscous fluid dynamics is discussed.
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An entropic interpolation problem for Incompressible viscid Fluids
Annales de l'Institut Henri Poincaré. Section B. Calculs des Probabilités et Statistiques, 2020Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscid Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general shape of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its connection with the Navier-Stokes equation is established.
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AN ENTROPIC INTERPOLATION PROBLEM FOR Incompressible VISCOUS Fluids
2019Co-Authors: Marc Arnaudon, Ana Bela Cruzeiro, Christian Léonard, Jean-claude ZambriniAbstract:In view of studying Incompressible Inviscid Fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966. Instead of Inviscid Fluids, the present paper is devoted to Incompressible viscous Fluids. A natural analogue of Brenier's problem is introduced, where generalized flows are no more supported by absolutely continuous paths, but by Brownian sample paths. It turns out that this new variational problem is an entropy minimization problem with marginal constraints entering the class of convex minimization problems. This paper explores the connection between this variational problem and Brenier's original problem. Its dual problem is derived and the general form of its solution is described. Under the restrictive assumption that the pressure is a nice function, the kinematics of its solution is made explicit and its relation with viscous fluid dynamics is discussed.
