2020

Farwig, Reinhard ; Kanamaru, Ryo (2020)
Optimality of Serrin type extension criteria to the Navier-Stokes equations.
In: Advances in Nonlinear Analysis, 10 (1)
doi: 10.1515/anona-2020-0130
Artikel, Bibliographie

2017

Farwig, Reinhard ; Kozono, Hideo ; Wegmann, David (2017)
Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data.
In: Journal of Mathematical Analysis and Applications, 453 (1)
doi: 10.1016/j.jmaa.2017.03.086
Artikel, Bibliographie

2016

Farwig, Reinhard ; Giga, Yoshikazu ; Hsu, Pen-Yuan (2016)
Initial Values for the Navier-Stokes Equations in Spaces with Weights in Time.
In: Funkcialaj Ekvacioj-Serio Internacia, 59 (2)
Artikel, Bibliographie

Farwig, Reinhard ; Rosteck, Veronika (2016)
Note on Friedrichs' inequality in N-star-shaped domains.
In: Journal of Mathematical Analysis and Applications, 435 (2)
Artikel, Bibliographie

Farwig, Reinhard ; Riechwald, Paul Felix (2016)
REGULARITY CRITERIA FOR WEAK SOLUTIONS OF THE NAVIER-STOKES SYSTEM IN GENERAL UNBOUNDED DOMAINS.
In: Discrete and Continuous Dynamical Systems-Series S, 9 (1)
Artikel, Bibliographie

Farwig, Reinhard ; Rosteck, Veronika (2016)
RESOLVENT ESTIMATES OF THE STOKES SYSTEM WITH NAVIER BOUNDARY CONDITIONS IN GENERAL UNBOUNDED DOMAINS.
In: Advances in Differential Equations, 21 (5-6)
Artikel, Bibliographie

2015

Farwig, Reinhard ; Nakatsuka, Tomoyuki ; Taniuchi, Yasushi (2015)
Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in L (3).
In: Archiv Der Mathematik, 104 (6)
Artikel, Bibliographie

Farwig, Reinhard ; Sohr, Hermann ; Varnhorn, Werner (2015)
LOCAL STRONG SOLUTIONS OF THE NONHOMOGENEOUS NAVIER-STOKES SYSTEM WITH CONTROL OF THE INTERVAL OF EXISTENCE.
In: Topological Methods in Nonlinear Analysis, 46 (2)
Artikel, Bibliographie

Farwig, Reinhard ; Nakatsuka, Tomoyuki ; Taniuchi, Yasushi (2015)
Uniqueness of Solutions on the Whole Time Axis to the Navier-Stokes Equations in Unbounded Domains.
In: Communications in Partial Differential Equations, 40 (10)
Artikel, Bibliographie

Farwig, Reinhard ; Riechwald, Paul Felix (2015)
Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains.
In: Nodea-Nonlinear Differential Equations and Applications, 22 (5)
Artikel, Bibliographie

Farwig, Reinhard ; Riechwald, Paul Felix (2015)
Very weak solutions to the Navier-Stokes system in general unbounded domains.
In: Journal of Evolution Equations, 15 (2)
Artikel, Bibliographie

2014

Farwig, Reinhard ; Sohr, Hermann ; Varnhorn, Werner (2014)
Besov Space Regularity Conditions for Weak Solutions of the Navier-Stokes Equations.
In: Journal of Mathematical Fluid Mechanics, 16
Artikel, Bibliographie

Farwig, Reinhard ; Kozono, Hideo (2014)
Weak solutions of the Navier-Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality.
In: Journal of Differential Equations, 256
Artikel, Bibliographie

Farwig, Reinhard ; Guenther, Ronald B. ; Thomann, Enrique A. ; Necasova, Sarka (2014)
THE FUNDAMENTAL SOLUTION OF LINEARIZED NONSTATIONARY NAVIER-STOKES EQUATIONS OF MOTION AROUND A ROTATING AND TRANSLATING BODY.
In: Discrete and Continuous Dynamical Systems, 34
Artikel, Bibliographie

Farwig, Reinhard ; Schulz, Raphael ; Yamazaki, Masao (2014)
Concentration-diffusion phenomena of heat convection in an incompressible fluid.
In: Asymptotic Analysis, 88
Artikel, Bibliographie

2013

Farwig, Reinhard ; Taniuchi, Yasushi (2013)
UNIQUENESS OF BACKWARD ASYMPTOTICALLY ALMOST PERIODIC-IN-TIME SOLUTIONS TO NAVIER-STOKES EQUATIONS IN UNBOUNDED DOMAINS.
In: Discrete and Continuous Dynamical Systems-Series S, 6
Artikel, Bibliographie

2012

Farwig, Reinhard ; Sohr, Hermann ; Varnhorn, Werner (2012)
Extensions of Serrin's Uniqueness and Regularity Conditions for the Navier-Stokes Equations.
In: Journal of Mathematical Fluid Mechanics, 14
Artikel, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Yanagisawa, Taku (2012)
Leray's inequality in general multi-connected domains in R-n.
In: Mathematische Annalen, 354
Artikel, Bibliographie

Farwig, Reinhard ; Morimoto, Hiroko (2012)
Leray's Inequality for Fluid Flow in Symmetric Multi-connected Two-dimensional Domains.
In: Tokyo Journal of Mathematics, 35
Artikel, Bibliographie

2011

Farwig, Reinhard ; Hishida, Toshiaki (2011)
Asymptotic profile of steady Stokes flow around a rotating obstacle.
In: Manuscripta Mathematica, 136
Artikel, Bibliographie

Farwig, Reinhard ; Hishida, Toshiaki (2011)
Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle.
In: Mathematische Nachrichten, 284
Artikel, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Kyed, Mads (2011)
ASYMPTOTIC STRUCTURE OF A LERAY SOLUTION TO THE NAVIER-STOKES FLOW AROUND A ROTATING BODY.
In: Pacific Journal of Mathematics, 253
Artikel, Bibliographie

Farwig, Reinhard ; Taniuchi, Yasushi (2011)
Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains.
In: Journal of Evolution Equations, 11
Artikel, Bibliographie

Farwig, Reinhard ; Necasova, Sarka ; Neustupa, Jiri (2011)
Spectral analysis of a Stokes-type operator arising from flow around a rotating body.
In: Journal of the Mathematical Society of Japan, 63
Artikel, Bibliographie

Farwig, Reinhard ; Sohr, Hermann ; Varnhorn, Werner (2011)
Necessary and sufficient conditions on local strong solvability of the Navier-Stokes system.
In: Applicable Analysis, 90
Artikel, Bibliographie

2010

Farwig, Reinhard ; Taniuchi, Yasushi (2010)
On the energy equality of Navier-Stokes equations in general unbounded domains.
In: Archiv Der Mathematik, 95
Artikel, Bibliographie

Farwig, Reinhard ; Sohr, Hermann (2010)
On the existence of local strong solutions for the Navier-Stokes equations in completely general domains.
In: Nonlinear Analysis-Theory Methods & Applications, 73
Artikel, Bibliographie

Farwig, Reinhard ; Komo, Christian (2010)
Regularity of weak solutions to the Navier-Stokes equations in exterior domains.
In: Nodea-Nonlinear Differential Equations and Applications, 17
Artikel, Bibliographie

Farwig, Reinhard ; Neustupa, Jiri (2010)
SPECTRAL PROPERTIES IN L-q OF AN OSEEN OPERATOR MODELLING FLUID FLOW PAST A ROTATING BODY.
In: Tohoku Mathematical Journal, 62
Artikel, Bibliographie

2007

Ri, Myong Hwan ; Farwig, Reinhard (2007)
Existence and exponential stability in L-r-spaces of stationary Navier-Stokes flows with prescribed flux in infinite cylindrical domains.
In: Mathematical Methods in the Applied Sciences, 30
Artikel, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann (2007)
Local in time regularity properties of the Navier-Stokes equations.
In: Indiana University Mathematics Journal, 56
Artikel, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann (2007)
On the Helmholtz decomposition in general unbounded domains.
In: Archiv der Mathematik, 88
Artikel, Bibliographie

Farwig, Reinhard ; Neustupa, Jiri (2007)
On the spectrum of a Stokes-type operator arising from flow around a rotating body.
In: Manuscripta Mathematica, 122
Artikel, Bibliographie

Farwig, Reinhard ; Hishida, T. (2007)
Stationary navier-stokes flow around a rotating obstacle.
In: Funkcialaj Ekvacioj : Serio Internacia, 50
Artikel, Bibliographie

Farwig, Reinhard ; Ri, Myong Hwan (2007)
Stokes resolvent systems in an infinite cylinder.
In: Mathematische Nachrichten, 280
Artikel, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann (2007)
Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data.
In: Journal of the Mathematical Society of Japan, 59
Artikel, Bibliographie

Farwig, Reinhard ; Myong-Hwan, Ri (2007)
The resolvent problem and H-infinity-calculus of the stokes operator in unbounded cylinders with several exits to infinity.
In: Journal of Evolution Equations, 7
Artikel, Bibliographie

2006

Farwig, Reinhard ; Myong-Hwan, Ri (2006)
Existence and exponential stability in L^r-spaces of stationary navier-Stokes flows with prescribed flux in infinite cylindrical domains.
Report, Bibliographie

Farwig, Reinhard (2006)
From weak to strong solutions of lthe Navier-Stokes equations in unbounded domains.
In: Scientific Transactions School of mathematics, Mongolian University of Science and Technology, 84
Artikel, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, Hermann (2006)
The Helmholtz decomposition in arbitrary unbounded domains : a theory beyond L2.
Konferenzveröffentlichung, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann (2006)
Local in time regularity properties of the Navier-Stokes equations.
In: Indiana University Mathematics Journal : Preprint 2465(2006) FB Mathematik TU Darmstadt. 20 S.
Artikel, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, Hermann (2006)
Very weak solutions and large uniqueness classes of stationary Navier-Stokes equations in bonded domains of R2.
In: Journal of Differential Equations, 227
Artikel, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, Hermann (2006)
A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data.
In: Journal of Mathematical Fluid Mechanics, 8
Artikel, Bibliographie

Farwig, Reinhard ; Myong-Hwan, Ri (2006)
The resolvent problem and H\infty-calculus of the Stokes operator in unbounded cylinders.
Report, Bibliographie

2005

Farwig, Reinhard (2005)
Flow around rotating obstacles : analysis of a singular integral operator.
Konferenzveröffentlichung, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann (2005)
The Helmholtz decomposition in arbitrary unbounded domains : a theory beyond L2.
Report, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, Hermann (2005)
Large Existence, Uniqueness and Regularity Classes of Stationary Navier-Stokes Equations in Bounded Domains of Rn.
Report, Bibliographie

Farwig, Reinhard ; Myong-Hwan, Ri (2005)
An Lq(L2)-Theory of the generalized stokes resolvent system in infinite cylinders.
Report, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann (2005)
An Lq-approach to Stokes and Navier-Stokes equations in general domains.
In: Acta Mathematica, 195
Artikel, Bibliographie

Farwig, Reinhard ; Neustupa, Jiri (2005)
On the spectrum of a stokes--type operator arising from flow around a rotating rody.
Report, Bibliographie

Farwig, Reinhard ; Myong-Hwan, Ri (2005)
Resolvent estimates and maximal regularity in weighted Lq-spaces of the Stokes operator in an infinite cylinder.
Report, Bibliographie

Farwig, Reinhard ; Myong-Hwan, Ri (2005)
Stokes Resolvent Systems in an Infinite Cylinder.
Report, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, Hermann (2005)
Very weak solutions and large uniqueness classes of stationary Navier-Stokes equations in bounded domains of R2.
Report, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, Hermann (2005)
Very weak solutions of stationary and instationary Navier-Stokes equations with nonhomogeneous data.
In: Nonlinear elliptic and parabolic problems : a special tribute to the work of Herbert Amann
Buchkapitel, Bibliographie

Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann (2005)
Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data.
Report, Bibliographie

Farwig, Reinhard ; Krbec, Miroslav ; Necasova, Sarka (2005)
A weighted Lq-approach to stokes flow around a rotating body.
Report, Bibliographie

Farwig, Reinhard (2005)
Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle.
In: Regularity and Other Aspects of the Navier-Stokes Equation
Buchkapitel, Bibliographie

2004

Farwig, Reinhard (2004)
An Lq-Analysis of Viscous Fluid Flow Past a Rotating Obstacle.
Buch, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, H. (2004)
Very weak solutions of stationary and instationary Navier-Stokes equations with nonhomogeneous data.
Buch, Bibliographie

Farwig, Reinhard ; Galdi, Giovanni P. ; Sohr, H. (2004)
A new class of weak solutions of Navier-Stokes equations with nonhomogeneous data.
Buch, Bibliographie

2003

Farwig, Reinhard (2003)
Existence of avalanching flows.
In: Dynamic response of granular and porous materials under large and catastrophic deformations / Kolumban Hutter ... (eds.).- Berlin[u.a.] : Springer, 2003, S. 219-249 (Lecture notes in applied and computational mechanics ; Vol. 11)
Artikel, Bibliographie

Farwig, Reinhard ; Hishida, Toshiaki ; Müller, Detlef (2003)
Lq-theory of a singular "winding" integral operator arising from fluid dynamics.
Buch, Bibliographie

Farwig, Reinhard (2003)
Weighted Lq-Helmholtz decompositions in infinite cylinders and in infinite layers.
In: Advances in differential equations, 8
Artikel, Bibliographie

2002

Farwig, Reinhard (2002)
Existence of avalanching flows.
Buch, Bibliographie

2000

Farwig, Reinhard ; Novotny, A. ; Pokorny, M. (2000)
The fundamental solution of a modified Oseen problem.
Buch, Bibliographie

1999

Farwig, Reinhard (1999)
Die (un-)berechenbare Angst des Mathematikers vor dem Fliegen.
In: Mathematische Semesterberichte. 46 (1999), S. 155-185
Artikel, Bibliographie

1998

Farwig, Reinhard (1998)
The stationary Navier-Stokes equations in a 3D-exterior domain.
In: Recent topics on mathematical theory of viscous incompressible fluid
Buchkapitel, Bibliographie

Farwig, Reinhard (1998)
(Rez.:) Lions, P.-L.: Mathematical topics in fluid mechanics. Vol. 1: Incompressible models. - Oxford: Clarendon Press, 1996.
In: SIAM Review. 40 (1998), 2
Artikel, Bibliographie

Farwig, Reinhard ; Sohr, (1998)
Weighted estimates for the Oseen equations and the Navier-Stokes equations in exterior domains.
In: Theory of the Navier-Stokes equations
Buchkapitel, Bibliographie

1997

Farwig, Reinhard (1997)
Weighted Lq-theory for the Stokes resolvent in exterior domains.
In: Journal of the Mathematical Society of Japan. 49 (1997), S. 251-288
Artikel, Bibliographie

Farwig, Reinhard (1997)
The stationary Navier-Stokes equation in a 3D-exterior domain.
Buch, Bibliographie

1996

Farwig, Reinhard ; Sohr, (1996)
Global estimates in weighted spaces of weak solutions of the Navier-Stokes equations in exterior domains.
In: Archiv der Mathematik. 67 (1996), S. 319-330
Artikel, Bibliographie

Farwig, Reinhard (1996)
Note on the flux condition and pressure drop in the resolvent problem of the Stokes system.
In: Manuscripta mathematica. 89 (1996), S. 139-158
Artikel, Bibliographie

Farwig, Reinhard (1996)
Partial regularity and weighted energy estimates of global weak solutions of the Navier-Stokes system.
In: Progress in partial differential equations: the Metz surveys 4
Buchkapitel, Bibliographie

1995

Farwig, Reinhard (1995)
Pressure drop and flux condition in the Lq-theory of the stokes resolvent problem in aperture domains.
In: Zeitschrift für angewandte Mathematik und Mechanik. 75 (1995), S. 457-458
Artikel, Bibliographie

Farwig, Reinhard ; Sohr, (1995)
Weighted Lq-theory of the stokes resolvent in exterior domains.
Buch, Bibliographie

Farwig, Reinhard ; Sohr, (1995)
Weighted energy inequalities for the Navier-Stokes equations in exterior domains.
In: Applicable analysis. 58 (1995), S. 157-173
Artikel, Bibliographie