Patrick Penel

981 total citations
45 papers, 458 citations indexed

About

Patrick Penel is a scholar working on Applied Mathematics, Mathematical Physics and Computational Mechanics. According to data from OpenAlex, Patrick Penel has authored 45 papers receiving a total of 458 indexed citations (citations by other indexed papers that have themselves been cited), including 37 papers in Applied Mathematics, 20 papers in Mathematical Physics and 12 papers in Computational Mechanics. Recurrent topics in Patrick Penel's work include Navier-Stokes equation solutions (34 papers), Advanced Mathematical Physics Problems (19 papers) and Stability and Controllability of Differential Equations (11 papers). Patrick Penel is often cited by papers focused on Navier-Stokes equation solutions (34 papers), Advanced Mathematical Physics Problems (19 papers) and Stability and Controllability of Differential Equations (11 papers). Patrick Penel collaborates with scholars based in France, Czechia and United States. Patrick Penel's co-authors include Milan Pokorný, Jiřı́ Neustupa, Šárka Nečasová, Stanislav Kračmar, Hamid Bellout, Emmanuel Duflos, Philippe Vanheeghe, P. L. Sulem, U. Frisch and Claude Bardos and has published in prestigious journals such as Journal of Mathematical Analysis and Applications, IEEE Transactions on Aerospace and Electronic Systems and Archive for Rational Mechanics and Analysis.

In The Last Decade

Patrick Penel

42 papers receiving 417 citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Patrick Penel France 12 366 225 171 157 87 45 458
Gabriela Planas Brazil 11 346 0.9× 150 0.7× 191 1.1× 128 0.8× 131 1.5× 34 461
C. Y. Chan United States 13 313 0.9× 123 0.5× 93 0.5× 66 0.4× 267 3.1× 70 529
G. A. Sviridyuk Russia 14 675 1.8× 392 1.7× 97 0.6× 74 0.5× 189 2.2× 56 831
Dalibor Pražák Czechia 10 129 0.4× 67 0.3× 186 1.1× 65 0.4× 165 1.9× 38 306
Reimund Rautmann Germany 7 125 0.3× 71 0.3× 48 0.3× 140 0.9× 67 0.8× 22 254
Daniel F. Shea United States 14 351 1.0× 178 0.8× 88 0.5× 59 0.4× 138 1.6× 29 571
Jiřı́ Neustupa Czechia 15 505 1.4× 256 1.1× 244 1.4× 213 1.4× 181 2.1× 72 589
Nadir Arada Portugal 10 83 0.2× 34 0.2× 96 0.6× 295 1.9× 298 3.4× 27 417
Giovanni Maria Troianiello Italy 6 282 0.8× 148 0.7× 47 0.3× 69 0.4× 296 3.4× 16 443
Xiaojing Xu China 18 844 2.3× 725 3.2× 421 2.5× 244 1.6× 86 1.0× 60 884

Countries citing papers authored by Patrick Penel

Since Specialization
Citations

This map shows the geographic impact of Patrick Penel's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Patrick Penel with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Patrick Penel more than expected).

Fields of papers citing papers by Patrick Penel

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Patrick Penel. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Patrick Penel. The network helps show where Patrick Penel may publish in the future.

Co-authorship network of co-authors of Patrick Penel

This figure shows the co-authorship network connecting the top 25 collaborators of Patrick Penel. A scholar is included among the top collaborators of Patrick Penel based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Patrick Penel. Patrick Penel is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Neustupa, Jiřı́ & Patrick Penel. (2014). Regularity of a Weak Solution to the Navier--Stokes Equations via One Component of a Spectral Projection of Vorticity. SIAM Journal on Mathematical Analysis. 46(2). 1681–1700. 4 indexed citations
2.
Kračmar, Stanislav, Šárka Nečasová, & Patrick Penel. (2013). A certain weighted variant of the embedding inequalities. Comptes Rendus Mathématique. 351(17-18). 663–668.
3.
Amrouche, Chérif, et al.. (2013). Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations. Annales mathématiques Blaise Pascal. 20(1). 37–73. 13 indexed citations
4.
Neustupa, Jiřı́ & Patrick Penel. (2012). Regularity criteria for weak solutions to the Navier–Stokes equations based on spectral projections of vorticity. Comptes Rendus Mathématique. 350(11-12). 597–602. 6 indexed citations
5.
Kračmar, Stanislav, Šárka Nečasová, & Patrick Penel. (2010). Anisotropic L 2 -estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body. Journal of the Mathematical Society of Japan. 62(1). 9 indexed citations
6.
Neustupa, Jiřı́ & Patrick Penel. (2010). Local in time strong solvability of the non-steady Navier–Stokes equations with Navier's boundary condition and the question of the inviscid limit. Comptes Rendus Mathématique. 348(19-20). 1093–1097. 6 indexed citations
7.
Kračmar, Stanislav, Šárka Nečasová, & Patrick Penel. (2010). 𝐿^{𝑞}-approach of weak solutions to stationary rotating Oseen equations in exterior domains. Quarterly of Applied Mathematics. 68(3). 421–437. 5 indexed citations
8.
Neustupa, Jiřı́ & Patrick Penel. (2009). The Navier–Stokes equations with Navier's boundary condition around moving bodies in presence of collisions. Comptes Rendus Mathématique. 347(11-12). 685–690. 5 indexed citations
9.
Bellout, Hamid, Jiřı́ Neustupa, & Patrick Penel. (2009). On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition. Comptes Rendus Mathématique. 347(19-20). 1141–1146. 7 indexed citations
10.
Neustupa, Jiřı́ & Patrick Penel. (2008). The Navier–Stokes equation with inhomogeneous boundary conditions based on vorticity. Banach Center Publications. 321–335. 4 indexed citations
11.
Kračmar, Stanislav, Šárka Nečasová, & Patrick Penel. (2008). Lq-approach to weak solutions of the Oseen flow around a rotating body. Banach Center Publications. 259–276. 6 indexed citations
12.
Penel, Patrick & Ivan Straškraba. (2007). Lyapunov analysis and stabilization to the rest state for solutions to the 1D-barotropic compressible Navier–Stokes equations. Comptes Rendus Mathématique. 345(2). 67–72. 1 indexed citations
13.
Nečasová, Šárka & Patrick Penel. (2006). Incompressible non‐Newtonian fluids: time asymptotic behaviour of weak solutions. Mathematical Methods in the Applied Sciences. 29(14). 1615–1630. 6 indexed citations
14.
Mucha, Piotr B., Patrick Penel, Michael Wiegner, & Wojciech M. Zajączkowski. (2005). Regularity and other aspects of the navier-stokes equations. 5 indexed citations
15.
Neustupa, Jiřı́ & Patrick Penel. (2004). On the regularity up to the boundary in the theory of the Navier–Stokes equations with generalized impermeability conditions. Comptes Rendus Mathématique. 340(1). 31–36. 2 indexed citations
16.
Neustupa, Jiřı́ & Patrick Penel. (2003). The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the Navier–Stokes equations. Comptes Rendus Mathématique. 336(10). 805–810. 15 indexed citations
17.
Neustupa, Jiřı́, et al.. (2001). Mathematical Fluid Mechanics. Birkhäuser Basel eBooks. 15 indexed citations
18.
Neustupa, Jiřı́ & Patrick Penel. (2001). Mathematical fluid mechanics : recent results and open questions. CERN Document Server (European Organization for Nuclear Research). 9 indexed citations
19.
Penel, Patrick, et al.. (1977). Sur une équation d'évolution non linéaire liée à la théorie de la turbulence. French digital mathematics library (Numdam). 4(1). 101–128. 2 indexed citations
20.
Penel, Patrick, et al.. (1974). Identification of parameters in a nonlinear self-consistent system including a Burgers' equation. Journal of Mathematical Analysis and Applications. 45(3). 654–681. 8 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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