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Mathematics Subject Classification – MSC2010

76-XX

Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX] 207342

76-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 147

76-01

Instructional exposition (textbooks, tutorial papers, etc.) 791

76-02

Research exposition (monographs, survey articles) 3703

76-03

Historical (must also be assigned at least one classification number from Section 01) 431

76-04

Explicit machine computation and programs (not the theory of computation or programming) 948

76-05

Experimental work 4509

76-06

Proceedings, conferences, collections, etc. 3078

76Axx

Foundations, constitutive equations, rheology 15397

76A02

Foundations of fluid mechanics 1089

76A05

Non-Newtonian fluids 5870

76A10

Viscoelastic fluids 4528

76A15

Liquid crystals [See also 82D30] 969

76A20

Thin fluid films 1524

76A25

Superfluids (classical aspects) 181

76A99

None of the above, but in this section 1667

76Bxx

Incompressible inviscid fluids 25337

76B03

Existence, uniqueness, and regularity theory [See also 35Q35] 1091

76B07

Free-surface potential flows 633

76B10

Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 4980

76B15

Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 9697

76B20

Ship waves 609

76B25

Solitary waves [See also 35C11] 1921

76B45

Capillarity (surface tension) [See also 76D45] 1091

76B47

Vortex flows 3539

76B55

Internal waves 1164

76B60

Atmospheric waves [See also 86A10] 542

76B65

Rossby waves [See also 86A05, 86A10] 421

76B70

Stratification effects in inviscid fluids 480

76B75

Flow control and optimization [See also 49Q10, 93C20, 93C95] 343

76B99

None of the above, but in this section 1896

76Dxx

Incompressible viscous fluids 40152

76D03

Existence, uniqueness, and regularity theory [See also 35Q30] 2706

76D05

Navier-Stokes equations [See also 35Q30] 18508

76D06

Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35] 224

76D07

Stokes and related (Oseen, etc.) flows 4532

76D08

Lubrication theory 1399

76D09

Viscous-inviscid interaction 168

76D10

Boundary-layer theory, separation and reattachment, higher-order effects 5885

76D17

Viscous vortex flows 1204

76D25

Wakes and jets 1538

76D27

Other free-boundary flows; Hele-Shaw flows 891

76D33

Waves 1192

76D45

Capillarity (surface tension) [See also 76B45] 1847

76D50

Stratification effects in viscous fluids 502

76D55

Flow control and optimization [See also 49Q10, 93C20, 93C95] 1064

76D99

None of the above, but in this section 3381

76Exx

Hydrodynamic stability 17239

76E05

Parallel shear flows 2722

76E06

Convection 1576

76E07

Rotation 772

76E09

Stability and instability of nonparallel flows 400

76E15

Absolute and convective instability and stability 2006

76E17

Interfacial stability and instability 1754

76E19

Compressibility effects 57

76E20

Stability and instability of geophysical and astrophysical flows 2271

76E25

Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 2845

76E30

Nonlinear effects 2640

76E99

None of the above, but in this section 3000

76Fxx

Turbulence [See also 37-XX, 60Gxx, 60Jxx] 18032

76F02

Fundamentals 361

76F05

Isotropic turbulence; homogeneous turbulence 2278

76F06

Transition to turbulence 709

76F10

Shear flows 3569

76F20

Dynamical systems approach to turbulence [See also 37-XX] 701

76F25

Turbulent transport, mixing 1592

76F30

Renormalization and other field-theoretical methods [See also 81T99] 98

76F35

Convective turbulence [See also 76E15, 76Rxx] 415

76F40

Turbulent boundary layers 1093

76F45

Stratification effects 296

76F50

Compressibility effects 344

76F55

Statistical turbulence modeling [See also 76M35] 1072

76F60

$k$-$\varepsilon$ modeling 980

76F65

Direct numerical and large eddy simulation of turbulence 3175

76F70

Control of turbulent flows 246

76F99

None of the above, but in this section 3588

76Gxx

General aerodynamics and subsonic flows 2746

76G25

General aerodynamics and subsonic flows 2728

76G99

None of the above, but in this section 14

76Hxx

Transonic flows 2474

76H05

Transonic flows 2473

76H99

None of the above, but in this section 1

76Jxx

Supersonic flows 2726

76J20

Supersonic flows 2719

76J99

None of the above, but in this section 4

76Kxx

Hypersonic flows 1346

76K05

Hypersonic flows 1346

76K99

None of the above, but in this section 0

76Lxx

Shock waves and blast waves [See also 35L67] 6891

76L05

Shock waves and blast waves [See also 35L67] 6878

76L99

None of the above, but in this section 8

76Mxx

Basic methods in fluid mechanics [See also 65-XX] 62872

76M10

Finite element methods 10927

76M12

Finite volume methods 5871

76M15

Boundary element methods 2178

76M20

Finite difference methods 11715

76M22

Spectral methods 1818

76M23

Vortex methods 385

76M25

Other numerical methods 11033

76M27

Visualization algorithms 185

76M28

Particle methods and lattice-gas methods 2925

76M30

Variational methods 1404

76M35

Stochastic analysis 1996

76M40

Complex-variables methods 461

76M45

Asymptotic methods, singular perturbations 2531

76M50

Homogenization 490

76M55

Dimensional analysis and similarity 689

76M60

Symmetry analysis, Lie group and algebra methods 649

76M99

None of the above, but in this section 11037

76Nxx

Compressible fluids and gas dynamics, general 16240

76N10

Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 5318

76N15

Gas dynamics, general 7485

76N17

Viscous-inviscid interaction 140

76N20

Boundary-layer theory 1682

76N25

Flow control and optimization 764

76N99

None of the above, but in this section 1087

76Pxx

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5681

76P05

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5674

76P99

None of the above, but in this section 5

76Qxx

Hydro- and aero-acoustics 8878

76Q05

Hydro- and aero-acoustics 8866

76Q99

None of the above, but in this section 9

76Rxx

Diffusion and convection 14485

76R05

Forced convection 2780

76R10

Free convection 6133

76R50

Diffusion [See also 60J60] 2940

76R99

None of the above, but in this section 3459

76Sxx

Flows in porous media; filtration; seepage 16789

76S05

Flows in porous media; filtration; seepage 16745

76S99

None of the above, but in this section 29

76Txx

Two-phase and multiphase flows 17507

76T10

Liquid-gas two-phase flows, bubbly flows 3666

76T15

Dusty-gas two-phase flows 736

76T20

Suspensions 1889

76T25

Granular flows [See also 74C99, 74E20] 897

76T30

Three or more component flows 720

76T99

None of the above, but in this section 8178

76Uxx

Rotating fluids 7001

76U05

Rotating fluids 6997

76U99

None of the above, but in this section 3

76Vxx

Reaction effects in flows [See also 80A32] 5570

76V05

Reaction effects in flows [See also 80A32] 5569

76V99

None of the above, but in this section 0

76Wxx

Magnetohydrodynamics and electrohydrodynamics 13571

76W05

Magnetohydrodynamics and electrohydrodynamics 13535

76W99

None of the above, but in this section 15

76Xxx

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6910

76X05

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6903

76X99

None of the above, but in this section 3

76Yxx

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2684

76Y05

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2678

76Y99

None of the above, but in this section 2

76Zxx

Biological fluid mechanics [See also 74F10, 74L15, 92Cxx] 4138

76Z05

Physiological flows [See also 92C35] 3151

76Z10

Biopropulsion in water and in air 579

76Z99

None of the above, but in this section 387

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Mathematics Subject Classification – MSC2010

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