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Papers by Hugo Da Veiga

Research paper thumbnail of An existence theorem in compressible fluid dynamics

Academie des Sciences Paris Comptes Rendus Serie B Sciences Physiques, Dec 1, 1979

Research paper thumbnail of Lineari Ellittiche Del Secondo Ordine

Research paper thumbnail of On the suitable weaksolutions to the Navier--Stokes equations in the whole space

Research paper thumbnail of Stationary motion and the incompressiblelimit for compressible viscous flows

Research paper thumbnail of Existence and Asymptotic Behavior for Strong Solutions of the Navier-Stokes Equations in the Whole Space

The IMA Volumes in Mathematics and Its Applications, 1987

Research paper thumbnail of Sur quelques inéquations paraboliques

Journal of Mathematical Analysis and Applications, 1974

Research paper thumbnail of Viscous incompressible flows under stress-free boundary conditions. The smoothness effect of near orthogonality or near parallelism between velocity and vorticity

Research paper thumbnail of On the extension to slip boundary conditions of a Bae and Choe regularity criterion for the Navier–Stokes equations. The half-space case

Journal of Mathematical Analysis and Applications, 2017

Research paper thumbnail of A missed persistence property for the Euler equations and its effect on inviscid limits

Research paper thumbnail of The 3-D Inviscid Limit Result Under Slip Boundary Conditions. A Negative Answer

Journal of Mathematical Fluid Mechanics, 2011

Research paper thumbnail of Sur la régularité des solutions de l'équation divA(x, u, ∇u)=B(x, u, ∇u) avec des conditions aux limites unilatérales et mêlées

Annali di Matematica Pura ed Applicata, Series 4, 1972

Research paper thumbnail of Remarks on the Navier–Stokes evolution equations under slip type boundary conditions with linear friction

Portugaliae Mathematica, 2007

Research paper thumbnail of Navier–Stokes equations: Green's matrices, vorticity direction, and regularity up to the boundary

Journal of Differential Equations, 2009

Research paper thumbnail of Continuité des solutions d'une inéquation parabolique

Research paper thumbnail of Structural stability and data dependencefor fully nonlinear hyperbolic problems

Research paper thumbnail of A remark on the differentiability for Green's operators of variational inequalities

Research paper thumbnail of Sul problema misto per le equazioni lineari ellittiche del secondo ordine

Research paper thumbnail of A Note on the Global Integrability, for Any Finite Power, of the Full Gradient for a Class of Power Law

In the following we show that weak solutions to a class of systems of power law type, p < 2 , ... more In the following we show that weak solutions to a class of systems of power law type, p < 2 , have integrable gradient up to the boundary, with any finite exponent. The above class covers some well known generalized Navier-Stokes systems with shear dependent viscosity. AMS subject classification 35Q30, 35K35, 76D03, 35K55. 1 Main result In the following we prove the W (Ω)-regularity up to the boundary, for any finite power q, for solutions of the system (1.4). The very weak assumptions made on the non-linear p-type term g(x,∇u) are compensated by the presence of the Laplace operator. However this situation often appears in the literature, in the presence of more stringent assumptions on the p-term. Actually, these assumptions can be easily generalized and the Laplace operator replaced by a non symmetric (non variational) elliptic operator. Our proof, based on a bootstrap argument and Stokes-elliptic regularization (see [4]) is elementary. In the sequel Ω is a bounded, connected, ...

Research paper thumbnail of Diffusion on Viscous Fluids. Existence and Asymptotic Properties of Solutions

Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 1983

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of On Time-Periodic Solutions of the Navier-Stokes Equations in Unbounded Cylindrical Domains. Leray’s Problem for Periodic Flows

Poiseuille flows in infinite cylindrical pipes, in spite of it enormous simplicity, have a main r... more Poiseuille flows in infinite cylindrical pipes, in spite of it enormous simplicity, have a main role in many theoretical and applied problems. As is well known, the Poiseuille flow is a stationary solution to the Stokes and the Navier-Stokes equations with a given constant flux. Time-periodic flows in channels and pipes have a comparable importance. However, the problem of the existence of time-periodic flows in correspondence to any given, time-periodic, total flux, is still an open problem. A solution is known only in some very particular cases as, for instance, the Womersley flows. Our aim is to solve this problem in the general case. This existence result open the way to further investigations, in particular by following in the footsteps of the stationary case. As an application, we present the first steps to the study of Leray’s problem for the Stokes and Navier-Stokes equations. We leave to the interested reader, or to forthcoming papers, the adaptation to time-periodic flows ...

Research paper thumbnail of An existence theorem in compressible fluid dynamics

Academie des Sciences Paris Comptes Rendus Serie B Sciences Physiques, Dec 1, 1979

Research paper thumbnail of Lineari Ellittiche Del Secondo Ordine

Research paper thumbnail of On the suitable weaksolutions to the Navier--Stokes equations in the whole space

Research paper thumbnail of Stationary motion and the incompressiblelimit for compressible viscous flows

Research paper thumbnail of Existence and Asymptotic Behavior for Strong Solutions of the Navier-Stokes Equations in the Whole Space

The IMA Volumes in Mathematics and Its Applications, 1987

Research paper thumbnail of Sur quelques inéquations paraboliques

Journal of Mathematical Analysis and Applications, 1974

Research paper thumbnail of Viscous incompressible flows under stress-free boundary conditions. The smoothness effect of near orthogonality or near parallelism between velocity and vorticity

Research paper thumbnail of On the extension to slip boundary conditions of a Bae and Choe regularity criterion for the Navier–Stokes equations. The half-space case

Journal of Mathematical Analysis and Applications, 2017

Research paper thumbnail of A missed persistence property for the Euler equations and its effect on inviscid limits

Research paper thumbnail of The 3-D Inviscid Limit Result Under Slip Boundary Conditions. A Negative Answer

Journal of Mathematical Fluid Mechanics, 2011

Research paper thumbnail of Sur la régularité des solutions de l'équation divA(x, u, ∇u)=B(x, u, ∇u) avec des conditions aux limites unilatérales et mêlées

Annali di Matematica Pura ed Applicata, Series 4, 1972

Research paper thumbnail of Remarks on the Navier–Stokes evolution equations under slip type boundary conditions with linear friction

Portugaliae Mathematica, 2007

Research paper thumbnail of Navier–Stokes equations: Green's matrices, vorticity direction, and regularity up to the boundary

Journal of Differential Equations, 2009

Research paper thumbnail of Continuité des solutions d'une inéquation parabolique

Research paper thumbnail of Structural stability and data dependencefor fully nonlinear hyperbolic problems

Research paper thumbnail of A remark on the differentiability for Green's operators of variational inequalities

Research paper thumbnail of Sul problema misto per le equazioni lineari ellittiche del secondo ordine

Research paper thumbnail of A Note on the Global Integrability, for Any Finite Power, of the Full Gradient for a Class of Power Law

In the following we show that weak solutions to a class of systems of power law type, p < 2 , ... more In the following we show that weak solutions to a class of systems of power law type, p < 2 , have integrable gradient up to the boundary, with any finite exponent. The above class covers some well known generalized Navier-Stokes systems with shear dependent viscosity. AMS subject classification 35Q30, 35K35, 76D03, 35K55. 1 Main result In the following we prove the W (Ω)-regularity up to the boundary, for any finite power q, for solutions of the system (1.4). The very weak assumptions made on the non-linear p-type term g(x,∇u) are compensated by the presence of the Laplace operator. However this situation often appears in the literature, in the presence of more stringent assumptions on the p-term. Actually, these assumptions can be easily generalized and the Laplace operator replaced by a non symmetric (non variational) elliptic operator. Our proof, based on a bootstrap argument and Stokes-elliptic regularization (see [4]) is elementary. In the sequel Ω is a bounded, connected, ...

Research paper thumbnail of Diffusion on Viscous Fluids. Existence and Asymptotic Properties of Solutions

Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 1983

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scien... more L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Research paper thumbnail of On Time-Periodic Solutions of the Navier-Stokes Equations in Unbounded Cylindrical Domains. Leray’s Problem for Periodic Flows

Poiseuille flows in infinite cylindrical pipes, in spite of it enormous simplicity, have a main r... more Poiseuille flows in infinite cylindrical pipes, in spite of it enormous simplicity, have a main role in many theoretical and applied problems. As is well known, the Poiseuille flow is a stationary solution to the Stokes and the Navier-Stokes equations with a given constant flux. Time-periodic flows in channels and pipes have a comparable importance. However, the problem of the existence of time-periodic flows in correspondence to any given, time-periodic, total flux, is still an open problem. A solution is known only in some very particular cases as, for instance, the Womersley flows. Our aim is to solve this problem in the general case. This existence result open the way to further investigations, in particular by following in the footsteps of the stationary case. As an application, we present the first steps to the study of Leray’s problem for the Stokes and Navier-Stokes equations. We leave to the interested reader, or to forthcoming papers, the adaptation to time-periodic flows ...

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