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Papers by Hugo Da Veiga
Academie des Sciences Paris Comptes Rendus Serie B Sciences Physiques, Dec 1, 1979
The IMA Volumes in Mathematics and Its Applications, 1987
Journal of Mathematical Analysis and Applications, 1974
Journal of Mathematical Analysis and Applications, 2017
Journal of Mathematical Fluid Mechanics, 2011
Annali di Matematica Pura ed Applicata, Series 4, 1972
Portugaliae Mathematica, 2007
Journal of Differential Equations, 2009
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, ...
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.
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 ...
Academie des Sciences Paris Comptes Rendus Serie B Sciences Physiques, Dec 1, 1979
The IMA Volumes in Mathematics and Its Applications, 1987
Journal of Mathematical Analysis and Applications, 1974
Journal of Mathematical Analysis and Applications, 2017
Journal of Mathematical Fluid Mechanics, 2011
Annali di Matematica Pura ed Applicata, Series 4, 1972
Portugaliae Mathematica, 2007
Journal of Differential Equations, 2009
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, ...
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.
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 ...