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Mathematics Subject Classification – MSC2010

76-XX

Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX] 209438

76-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 148

76-01

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

76-02

Research exposition (monographs, survey articles) 3713

76-03

Historical (must also be assigned at least one classification number from Section 01) 436

76-04

Explicit machine computation and programs (not the theory of computation or programming) 989

76-05

Experimental work 4525

76-06

Proceedings, conferences, collections, etc. 3016

76Axx

Foundations, constitutive equations, rheology 15483

76A02

Foundations of fluid mechanics 1094

76A05

Non-Newtonian fluids 5913

76A10

Viscoelastic fluids 4556

76A15

Liquid crystals [See also 82D30] 977

76A20

Thin fluid films 1543

76A25

Superfluids (classical aspects) 182

76A99

None of the above, but in this section 1672

76Bxx

Incompressible inviscid fluids 25463

76B03

Existence, uniqueness, and regularity theory [See also 35Q35] 1104

76B07

Free-surface potential flows 641

76B10

Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 4995

76B15

Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 9750

76B20

Ship waves 613

76B25

Solitary waves [See also 35C11] 1928

76B45

Capillarity (surface tension) [See also 76D45] 1101

76B47

Vortex flows 3551

76B55

Internal waves 1171

76B60

Atmospheric waves [See also 86A10] 543

76B65

Rossby waves [See also 86A05, 86A10] 423

76B70

Stratification effects in inviscid fluids 483

76B75

Flow control and optimization [See also 49Q10, 93C20, 93C95] 345

76B99

None of the above, but in this section 1898

76Dxx

Incompressible viscous fluids 40569

76D03

Existence, uniqueness, and regularity theory [See also 35Q30] 2721

76D05

Navier-Stokes equations [See also 35Q30] 18774

76D06

Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35] 229

76D07

Stokes and related (Oseen, etc.) flows 4573

76D08

Lubrication theory 1405

76D09

Viscous-inviscid interaction 173

76D10

Boundary-layer theory, separation and reattachment, higher-order effects 5911

76D17

Viscous vortex flows 1223

76D25

Wakes and jets 1558

76D27

Other free-boundary flows; Hele-Shaw flows 900

76D33

Waves 1199

76D45

Capillarity (surface tension) [See also 76B45] 1871

76D50

Stratification effects in viscous fluids 504

76D55

Flow control and optimization [See also 49Q10, 93C20, 93C95] 1083

76D99

None of the above, but in this section 3385

76Exx

Hydrodynamic stability 17286

76E05

Parallel shear flows 2733

76E06

Convection 1585

76E07

Rotation 772

76E09

Stability and instability of nonparallel flows 404

76E15

Absolute and convective instability and stability 2009

76E17

Interfacial stability and instability 1758

76E19

Compressibility effects 58

76E20

Stability and instability of geophysical and astrophysical flows 2278

76E25

Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 2852

76E30

Nonlinear effects 2644

76E99

None of the above, but in this section 3004

76Fxx

Turbulence [See also 37-XX, 60Gxx, 60Jxx] 18335

76F02

Fundamentals 365

76F05

Isotropic turbulence; homogeneous turbulence 2283

76F06

Transition to turbulence 719

76F10

Shear flows 3574

76F20

Dynamical systems approach to turbulence [See also 37-XX] 707

76F25

Turbulent transport, mixing 1612

76F30

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

76F35

Convective turbulence [See also 76E15, 76Rxx] 418

76F40

Turbulent boundary layers 1107

76F45

Stratification effects 302

76F50

Compressibility effects 357

76F55

Statistical turbulence modeling [See also 76M35] 1084

76F60

$k$-$\varepsilon$ modeling 1001

76F65

Direct numerical and large eddy simulation of turbulence 3400

76F70

Control of turbulent flows 248

76F99

None of the above, but in this section 3596

76Gxx

General aerodynamics and subsonic flows 2804

76G25

General aerodynamics and subsonic flows 2785

76G99

None of the above, but in this section 14

76Hxx

Transonic flows 2492

76H05

Transonic flows 2491

76H99

None of the above, but in this section 1

76Jxx

Supersonic flows 2753

76J20

Supersonic flows 2746

76J99

None of the above, but in this section 4

76Kxx

Hypersonic flows 1361

76K05

Hypersonic flows 1361

76K99

None of the above, but in this section 0

76Lxx

Shock waves and blast waves [See also 35L67] 6958

76L05

Shock waves and blast waves [See also 35L67] 6945

76L99

None of the above, but in this section 8

76Mxx

Basic methods in fluid mechanics [See also 65-XX] 63952

76M10

Finite element methods 11155

76M12

Finite volume methods 6175

76M15

Boundary element methods 2196

76M20

Finite difference methods 11909

76M22

Spectral methods 1865

76M23

Vortex methods 389

76M25

Other numerical methods 11210

76M27

Visualization algorithms 188

76M28

Particle methods and lattice-gas methods 3104

76M30

Variational methods 1407

76M35

Stochastic analysis 2007

76M40

Complex-variables methods 463

76M45

Asymptotic methods, singular perturbations 2539

76M50

Homogenization 490

76M55

Dimensional analysis and similarity 693

76M60

Symmetry analysis, Lie group and algebra methods 656

76M99

None of the above, but in this section 11029

76Nxx

Compressible fluids and gas dynamics, general 16445

76N10

Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 5349

76N15

Gas dynamics, general 7569

76N17

Viscous-inviscid interaction 144

76N20

Boundary-layer theory 1693

76N25

Flow control and optimization 773

76N99

None of the above, but in this section 1096

76Pxx

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5726

76P05

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5719

76P99

None of the above, but in this section 5

76Qxx

Hydro- and aero-acoustics 8930

76Q05

Hydro- and aero-acoustics 8918

76Q99

None of the above, but in this section 9

76Rxx

Diffusion and convection 14548

76R05

Forced convection 2790

76R10

Free convection 6166

76R50

Diffusion [See also 60J60] 2955

76R99

None of the above, but in this section 3461

76Sxx

Flows in porous media; filtration; seepage 16945

76S05

Flows in porous media; filtration; seepage 16901

76S99

None of the above, but in this section 31

76Txx

Two-phase and multiphase flows 17738

76T10

Liquid-gas two-phase flows, bubbly flows 3753

76T15

Dusty-gas two-phase flows 741

76T20

Suspensions 1951

76T25

Granular flows [See also 74C99, 74E20] 919

76T30

Three or more component flows 730

76T99

None of the above, but in this section 8207

76Uxx

Rotating fluids 7036

76U05

Rotating fluids 7031

76U99

None of the above, but in this section 3

76Vxx

Reaction effects in flows [See also 80A32] 5605

76V05

Reaction effects in flows [See also 80A32] 5604

76V99

None of the above, but in this section 0

76Wxx

Magnetohydrodynamics and electrohydrodynamics 13680

76W05

Magnetohydrodynamics and electrohydrodynamics 13645

76W99

None of the above, but in this section 15

76Xxx

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6931

76X05

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6924

76X99

None of the above, but in this section 3

76Yxx

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2701

76Y05

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2695

76Y99

None of the above, but in this section 2

76Zxx

Biological fluid mechanics [See also 74F10, 74L15, 92Cxx] 4233

76Z05

Physiological flows [See also 92C35] 3220

76Z10

Biopropulsion in water and in air 607

76Z99

None of the above, but in this section 388

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Mathematics Subject Classification – MSC2010

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