Tools

LEADER 04971cam a2200565 i 4500

001 on1342509429;

003 OCoLC;

005 20221130103919.0;

008 220623s2022 riua b 001 0 eng ;

010 a| 2022025318;

020 a| 9781470470494q| hardcover;

020 a| 1470470497q| hardcover;

020 a| 9781470471781q| paperback;

020 a| 1470471787q| paperback;

020 z| 9781470471774q| electronic book;

035 a| (Sirsi) o1342509429;

035 a| (OCoLC)1342509429;

042 a| pcc;

049 a| EREE;

050 00 a| QA911b| .B33 2022;

082 00 a| 532/.0501518642| 23/eng20220826;

084 a| 35Q30a| 35Q31a| 35Q35a| 76Bxxa| 76Dxxa| 76E052| msc;

100 1 a| Bedrossian, Jacob,d| 1984-e| author.=| ^A1446574;

245 14 a| The mathematical analysis of the incompressible Euler and Navier-Stokes equations :b| an introduction /c| Jacob Bedrossian, Vlad Vicol.;

264 1 a| Providence, Rhode Island :b| American Mathematical Society,c| [2022];

300 a| xiii, 218 pages :b| illustrations ;c| 27 cm.;

336 a| textb| txt2| rdacontent;

337 a| unmediatedb| n2| rdamedia;

338 a| volumeb| nc2| rdacarrier;

490 1 a| Graduate studies in mathematics,x| 1065-7339 ;v| 225;

504 a| Includes bibliographical references (pages 199-216) and index.;

505 0 a| Preface -- Ideal incompressible fluids: the Euler equations -- Eulerian vs Lagrangian representations -- Incompressibility and Transport -- The incompressible homogeneous Euler equations -- Vorticity -- Symmetries and conservation laws -- Special explicit solutions -- Exercises -- Existence of solutions and continuation criteria for Euler -- Local existence of Hs solutions -- The Lipschitz continuation criterion -- The Beale-Kato-Majda theorem -- The global existence of strong solutions in 2D -- The Constantin-Fefferman-Majda criterion -- Exercises -- Incompressible viscous fluids: the Navier-Stokes equations -- Viscosity -- Non-dimensionalization -- Vorticity, symmetries, and balance laws -- Special explicit solutions -- Local existence of Hs solutions -- Strong solutions with initial datum in H1 : local and global -- Exercises -- Leray-Hopf weak solutions of Navier-Stokes -- Weak solutions -- Existence of weak solutions on the whole space via mollification -- The uniqueness of weak solutions in 2D -- Weak-strong uniqueness and the Prodi-Serrin class -- Partial regularity in time for Leray-Hopf weak solutions -- Existence of weak solutions on the periodic box via Galerkin -- Exercises -- Mild solutions of Navier-Stokes -- Mild formulation -- Scaling criticality -- Local-in-time well-posedness in H 1/2 -- Local-in-time well-posedness in L3 -- Local regularization -- Continuation of smooth solutions -- Exercises -- A survey of some advanced topics -- Local regularity and the Prodi-Serrin conditions -- Partial regularity of suitable weak solutions in 3D -- Bounded domains -- Stationary solutions of the Navier-Stokes equations -- Ruling out backward self-similar finite-time singularities -- Critical and supercritical well-posedness for Navier-Stokes -- Yudovich theory and 2D Euler with Lp vorticity -- Gradient growth in the 2D Euler equations -- The search for finite-time singularties in 3D Euler -- Hydrodynamic stability: Euler -- Hydrodynamic stability: Navier-Stokes -- The energy balance and Onsager's conjecture -- Appendix -- The contraction mapping principle -- Existence and uniqueness for ODEs -- Fourier transform -- Integral operators -- Sobolev Spaces -- Basic properties of the Poisson and heat equations -- Mollifiers -- Sobolev and Gagliardo-Nirenberg inequalities -- Compactness -- Bibliography -- Index.;

650 0 a| Fluid dynamics.=| ^A18739;

650 0 a| Navier-Stokes equations.=| ^A79119;

650 7 a| Fluid dynamics.2| fast0| (OCoLC)fst00927973;

650 7 a| Navier-Stokes equations.2| fast0| (OCoLC)fst01035071;

650 7 a| Partial differential equations -- Equations of mathematical physics and other areas of application -- Navier-Stokes equations.2| msc;

650 7 a| Partial differential equations -- Equations of mathematical physics and other areas of application -- Euler equations.2| msc;

650 7 a| Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with fluid mechanics.2| msc;

650 7 a| Fluid mechanics -- Incompressible inviscid fluids.2| msc;

650 7 a| Fluid mechanics -- Incompressible viscous fluids.2| msc;

650 7 a| Fluid mechanics -- Hydrodynamic stability -- Parallel shear flows.2| msc;

700 1 a| Vicol, Vlad,d| 1983-e| author.=| ^A1450277;

830 0 a| Graduate studies in mathematics ;v| v. 225.=| ^A347883;

949 a| QA911 .B33 2022h| JOYNER48o| jssb;

994 a| C0b| ERE;

596 a| 1;

998 a| 5929209;

999 a| QA911 .B33 2022w| LCc| 1i| 30372017356848d| 6/15/2023e| 4/17/2023l| JGESm| JOYNERn| 1r| Ys| Yt| JGESBKu| 10/19/2022x| BOOKz| JSTACKSo| .STAFF. jjlm;

The mathematical analysis of the incompressible Euler and Navier-Stokes equations : an introduction / Jacob Bedrossian, Vlad Vicol.

Author/creator	Bedrossian, Jacob, 1984- author.
Other author	Vicol, Vlad, 1983- author.
Format	Book
Publication	Providence, Rhode Island : American Mathematical Society, [2022]
Description	xiii, 218 pages : illustrations ; 27 cm.
Subjects	Fluid dynamics. Navier-Stokes equations.

Series	Graduate studies in mathematics, 1065-7339 ; 225 Graduate studies in mathematics ; v. 225. ^A347883
Contents	Preface -- Ideal incompressible fluids: the Euler equations -- Eulerian vs Lagrangian representations -- Incompressibility and Transport -- The incompressible homogeneous Euler equations -- Vorticity -- Symmetries and conservation laws -- Special explicit solutions -- Exercises -- Existence of solutions and continuation criteria for Euler -- Local existence of Hs solutions -- The Lipschitz continuation criterion -- The Beale-Kato-Majda theorem -- The global existence of strong solutions in 2D -- The Constantin-Fefferman-Majda criterion -- Exercises -- Incompressible viscous fluids: the Navier-Stokes equations -- Viscosity -- Non-dimensionalization -- Vorticity, symmetries, and balance laws -- Special explicit solutions -- Local existence of Hs solutions -- Strong solutions with initial datum in H1 : local and global -- Exercises -- Leray-Hopf weak solutions of Navier-Stokes -- Weak solutions -- Existence of weak solutions on the whole space via mollification -- The uniqueness of weak solutions in 2D -- Weak-strong uniqueness and the Prodi-Serrin class -- Partial regularity in time for Leray-Hopf weak solutions -- Existence of weak solutions on the periodic box via Galerkin -- Exercises -- Mild solutions of Navier-Stokes -- Mild formulation -- Scaling criticality -- Local-in-time well-posedness in H 1/2 -- Local-in-time well-posedness in L3 -- Local regularization -- Continuation of smooth solutions -- Exercises -- A survey of some advanced topics -- Local regularity and the Prodi-Serrin conditions -- Partial regularity of suitable weak solutions in 3D -- Bounded domains -- Stationary solutions of the Navier-Stokes equations -- Ruling out backward self-similar finite-time singularities -- Critical and supercritical well-posedness for Navier-Stokes -- Yudovich theory and 2D Euler with Lp vorticity -- Gradient growth in the 2D Euler equations -- The search for finite-time singularties in 3D Euler -- Hydrodynamic stability: Euler -- Hydrodynamic stability: Navier-Stokes -- The energy balance and Onsager's conjecture -- Appendix -- The contraction mapping principle -- Existence and uniqueness for ODEs -- Fourier transform -- Integral operators -- Sobolev Spaces -- Basic properties of the Poisson and heat equations -- Mollifiers -- Sobolev and Gagliardo-Nirenberg inequalities -- Compactness -- Bibliography -- Index.
Bibliography note	Includes bibliographical references (pages 199-216) and index.
LCCN	2022025318
ISBN	9781470470494 hardcover
ISBN	1470470497 hardcover
ISBN	9781470471781 paperback
ISBN	1470471787 paperback
ISBN	electronic book

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The mathematical analysis of the incompressible Euler and Navier-Stokes equations : an introduction / Jacob Bedrossian, Vlad Vicol.

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