國立虎尾科技大學 |

Navier–Stokes Equations = An Introduction with Applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Navier–Stokes Equations/ by Grzegorz Łukaszewicz, Piotr Kalita.
其他題名:	An Introduction with Applications /
作者:	Łukaszewicz, Grzegorz.
其他作者:	Kalita, Piotr.
面頁冊數:	XIV, 390 p. 24 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Partial differential equations. -
電子資源:	https://doi.org/10.1007/978-3-319-27760-8
ISBN:	9783319277608

Navier–Stokes Equations = An Introduction with Applications /
Łukaszewicz, Grzegorz.

Navier–Stokes EquationsAn Introduction with Applications /[electronic resource] :by Grzegorz Łukaszewicz, Piotr Kalita. - 1st ed. 2016. - XIV, 390 p. 24 illus.online resource. - Advances in Mechanics and Mathematics,1571-8689. - Advances in Mechanics and Mathematics,33.

Introduction and summary -- Equations of classical hydrodynamics -- Mathematical preliminaries -- Stationary solutions of the Navier–Stokes equations -- Stationary solutions of the Navier–Stokes equations with friction -- Stationary flows in narrow films and the Reynolds equation -- Autonomous two-dimensional Navier–Stokes equations -- Invariant measures and statistical solutions -- Global attractors and a lubrication problem -- Exponential attractors in contact problems -- Non-autonomous Navier–Stokes equations and pullback attractors -- Pullback attractors and statistical solutions -- Pullback attractors and shear flows -- Trajectory attractors and feedback boundary control in contact problems.-Evolutionary systems and the Navier–Stokes equations -- Attractors for multivalued processes in contact problems -- References -- Index.

This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.

ISBN: 9783319277608

Standard No.: 10.1007/978-3-319-27760-8doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Navier–Stokes Equations = An Introduction with Applications /
LDR:04246nam a22004095i 4500 001 971157
003 DE-He213
005 20200701175401.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319277608 $9 978-3-319-27760-8
024 7 $a 10.1007/978-3-319-27760-8 $2 doi
035 $a 978-3-319-27760-8
050 4 $a QA370-380
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
100 1 $a Łukaszewicz, Grzegorz. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1266689
245 1 0 $a Navier–Stokes Equations $h [electronic resource] : $b An Introduction with Applications / $c by Grzegorz Łukaszewicz, Piotr Kalita.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XIV, 390 p. 24 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Advances in Mechanics and Mathematics, $x 1571-8689
505 0 $a Introduction and summary -- Equations of classical hydrodynamics -- Mathematical preliminaries -- Stationary solutions of the Navier–Stokes equations -- Stationary solutions of the Navier–Stokes equations with friction -- Stationary flows in narrow films and the Reynolds equation -- Autonomous two-dimensional Navier–Stokes equations -- Invariant measures and statistical solutions -- Global attractors and a lubrication problem -- Exponential attractors in contact problems -- Non-autonomous Navier–Stokes equations and pullback attractors -- Pullback attractors and statistical solutions -- Pullback attractors and shear flows -- Trajectory attractors and feedback boundary control in contact problems.-Evolutionary systems and the Navier–Stokes equations -- Attractors for multivalued processes in contact problems -- References -- Index.
520 $a This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.
650 0 $a Partial differential equations. $3 1102982
650 0 $a Differential equations. $3 527664
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Fluid mechanics. $3 555551
650 1 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Engineering Fluid Dynamics. $3 670525
700 1 $a Kalita, Piotr. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1108181
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319277585
776 0 8 $i Printed edition: $z 9783319277592
776 0 8 $i Printed edition: $z 9783319802107
830 0 $a Advances in Mechanics and Mathematics, $x 1571-8689 ; $v 33 $3 1261614
856 4 0 $u https://doi.org/10.1007/978-3-319-27760-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)