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Mathematics Subject Classification – MSC2010

76-XX

Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX] 213914

76-00

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

76-01

Instructional exposition (textbooks, tutorial papers, etc.) 804

76-02

Research exposition (monographs, survey articles) 3741

76-03

Historical (must also be assigned at least one classification number from Section 01) 447

76-04

Explicit machine computation and programs (not the theory of computation or programming) 995

76-05

Experimental work 4569

76-06

Proceedings, conferences, collections, etc. 3032

76Axx

Foundations, constitutive equations, rheology 15784

76A02

Foundations of fluid mechanics 1103

76A05

Non-Newtonian fluids 6057

76A10

Viscoelastic fluids 4617

76A15

Liquid crystals [See also 82D30] 1013

76A20

Thin fluid films 1595

76A25

Superfluids (classical aspects) 186

76A99

None of the above, but in this section 1678

76Bxx

Incompressible inviscid fluids 25731

76B03

Existence, uniqueness, and regularity theory [See also 35Q35] 1134

76B07

Free-surface potential flows 651

76B10

Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 5022

76B15

Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 9871

76B20

Ship waves 618

76B25

Solitary waves [See also 35C11] 1951

76B45

Capillarity (surface tension) [See also 76D45] 1120

76B47

Vortex flows 3582

76B55

Internal waves 1181

76B60

Atmospheric waves [See also 86A10] 544

76B65

Rossby waves [See also 86A05, 86A10] 424

76B70

Stratification effects in inviscid fluids 486

76B75

Flow control and optimization [See also 49Q10, 93C20, 93C95] 353

76B99

None of the above, but in this section 1903

76Dxx

Incompressible viscous fluids 41197

76D03

Existence, uniqueness, and regularity theory [See also 35Q30] 2789

76D05

Navier-Stokes equations [See also 35Q30] 19094

76D06

Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35] 230

76D07

Stokes and related (Oseen, etc.) flows 4678

76D08

Lubrication theory 1427

76D09

Viscous-inviscid interaction 177

76D10

Boundary-layer theory, separation and reattachment, higher-order effects 5955

76D17

Viscous vortex flows 1246

76D25

Wakes and jets 1574

76D27

Other free-boundary flows; Hele-Shaw flows 912

76D33

Waves 1215

76D45

Capillarity (surface tension) [See also 76B45] 1890

76D50

Stratification effects in viscous fluids 507

76D55

Flow control and optimization [See also 49Q10, 93C20, 93C95] 1114

76D99

None of the above, but in this section 3398

76Exx

Hydrodynamic stability 17392

76E05

Parallel shear flows 2742

76E06

Convection 1607

76E07

Rotation 784

76E09

Stability and instability of nonparallel flows 408

76E15

Absolute and convective instability and stability 2012

76E17

Interfacial stability and instability 1770

76E19

Compressibility effects 61

76E20

Stability and instability of geophysical and astrophysical flows 2292

76E25

Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 2862

76E30

Nonlinear effects 2654

76E99

None of the above, but in this section 3014

76Fxx

Turbulence [See also 37-XX, 60Gxx, 60Jxx] 18549

76F02

Fundamentals 378

76F05

Isotropic turbulence; homogeneous turbulence 2300

76F06

Transition to turbulence 726

76F10

Shear flows 3591

76F20

Dynamical systems approach to turbulence [See also 37-XX] 722

76F25

Turbulent transport, mixing 1630

76F30

Renormalization and other field-theoretical methods [See also 81T99] 101

76F35

Convective turbulence [See also 76E15, 76Rxx] 425

76F40

Turbulent boundary layers 1124

76F45

Stratification effects 307

76F50

Compressibility effects 361

76F55

Statistical turbulence modeling [See also 76M35] 1100

76F60

$k$-$\varepsilon$ modeling 1016

76F65

Direct numerical and large eddy simulation of turbulence 3480

76F70

Control of turbulent flows 256

76F99

None of the above, but in this section 3604

76Gxx

General aerodynamics and subsonic flows 2856

76G25

General aerodynamics and subsonic flows 2833

76G99

None of the above, but in this section 14

76Hxx

Transonic flows 2501

76H05

Transonic flows 2500

76H99

None of the above, but in this section 1

76Jxx

Supersonic flows 2772

76J20

Supersonic flows 2763

76J99

None of the above, but in this section 4

76Kxx

Hypersonic flows 1368

76K05

Hypersonic flows 1368

76K99

None of the above, but in this section 0

76Lxx

Shock waves and blast waves [See also 35L67] 7023

76L05

Shock waves and blast waves [See also 35L67] 7004

76L99

None of the above, but in this section 8

76Mxx

Basic methods in fluid mechanics [See also 65-XX] 64809

76M10

Finite element methods 11396

76M12

Finite volume methods 6265

76M15

Boundary element methods 2213

76M20

Finite difference methods 12029

76M22

Spectral methods 1896

76M23

Vortex methods 392

76M25

Other numerical methods 11394

76M27

Visualization algorithms 197

76M28

Particle methods and lattice-gas methods 3191

76M30

Variational methods 1415

76M35

Stochastic analysis 2028

76M40

Complex-variables methods 465

76M45

Asymptotic methods, singular perturbations 2558

76M50

Homogenization 502

76M55

Dimensional analysis and similarity 700

76M60

Symmetry analysis, Lie group and algebra methods 670

76M99

None of the above, but in this section 11040

76Nxx

Compressible fluids and gas dynamics, general 16649

76N10

Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 5412

76N15

Gas dynamics, general 7659

76N17

Viscous-inviscid interaction 148

76N20

Boundary-layer theory 1701

76N25

Flow control and optimization 804

76N99

None of the above, but in this section 1098

76Pxx

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5771

76P05

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5761

76P99

None of the above, but in this section 5

76Qxx

Hydro- and aero-acoustics 9025

76Q05

Hydro- and aero-acoustics 9010

76Q99

None of the above, but in this section 10

76Rxx

Diffusion and convection 14707

76R05

Forced convection 2814

76R10

Free convection 6247

76R50

Diffusion [See also 60J60] 3006

76R99

None of the above, but in this section 3470

76Sxx

Flows in porous media; filtration; seepage 17309

76S05

Flows in porous media; filtration; seepage 17260

76S99

None of the above, but in this section 33

76Txx

Two-phase and multiphase flows 17938

76T10

Liquid-gas two-phase flows, bubbly flows 3815

76T15

Dusty-gas two-phase flows 750

76T20

Suspensions 2013

76T25

Granular flows [See also 74C99, 74E20] 931

76T30

Three or more component flows 744

76T99

None of the above, but in this section 8239

76Uxx

Rotating fluids 7101

76U05

Rotating fluids 7094

76U99

None of the above, but in this section 4

76Vxx

Reaction effects in flows [See also 80A32] 5681

76V05

Reaction effects in flows [See also 80A32] 5678

76V99

None of the above, but in this section 0

76Wxx

Magnetohydrodynamics and electrohydrodynamics 13935

76W05

Magnetohydrodynamics and electrohydrodynamics 13898

76W99

None of the above, but in this section 15

76Xxx

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6979

76X05

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6971

76X99

None of the above, but in this section 3

76Yxx

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2738

76Y05

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2733

76Y99

None of the above, but in this section 2

76Zxx

Biological fluid mechanics [See also 74F10, 74L15, 92Cxx] 4376

76Z05

Physiological flows [See also 92C35] 3334

76Z10

Biopropulsion in water and in air 628

76Z99

None of the above, but in this section 396

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Mathematics Subject Classification – MSC2010

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