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Mathematics Subject Classification – MSC2020

76-XX

Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} 221665

76-00

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to fluid mechanics 149

76-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics 822

76-02

Research exposition (monographs, survey articles) pertaining to fluid mechanics 3821

76-03

History of fluid mechanics [Consider also classification numbers pertaining to Section 01-XX] 472

76-04

Software, source code, etc. for problems pertaining to fluid mechanics 1064

76-05

Experimental work for problems pertaining to fluid mechanics 4752

76-06

Proceedings, conferences, collections, etc. pertaining to fluid mechanics 3043

76-10

Mathematical modeling or simulation for problems pertaining to fluid mechanics 39

76-11

Research data for problems pertaining to fluid mechanics 0

76Axx

Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena 16571

76A02

Foundations of fluid mechanics 1146

76A05

Non-Newtonian fluids 6369

76A10

Viscoelastic fluids 4811

76A15

Liquid crystals [See also 82D30] 1088

76A20

Thin fluid films 1780

76A25

Superfluids (classical aspects) 198

76A30

Traffic and pedestrian flow models 1

76A99

None of the above, but in this section 1693

76Bxx

Incompressible inviscid fluids 26938

76B03

Existence, uniqueness, and regularity theory for incompressible inviscid fluids [See also 35Q35] 1239

76B07

Free-surface potential flows for incompressible inviscid fluids 714

76B10

Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 5182

76B15

Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 10435

76B20

Ship waves 652

76B25

Solitary waves for incompressible inviscid fluids [See also 35C11] 2040

76B45

Capillarity (surface tension) for incompressible inviscid fluids [See also 76D45] 1192

76B47

Vortex flows for incompressible inviscid fluids 3742

76B55

Internal waves for incompressible inviscid fluids 1235

76B70

Stratification effects in inviscid fluids 543

76B75

Flow control and optimization for incompressible inviscid fluids [See also 49Q10, 93C20, 93C95] 377

76B99

None of the above, but in this section 1928

76Dxx

Incompressible viscous fluids 43626

76D03

Existence, uniqueness, and regularity theory for incompressible viscous fluids [See also 35Q30] 3016

76D05

Navier-Stokes equations for incompressible viscous fluids [See also 35Q30] 20271

76D06

Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35] 246

76D07

Stokes and related (Oseen, etc.) flows 5042

76D08

Lubrication theory 1530

76D09

Viscous-inviscid interaction 185

76D10

Boundary-layer theory, separation and reattachment, higher-order effects 6123

76D17

Viscous vortex flows 1425

76D25

Wakes and jets 1732

76D27

Other free boundary flows; Hele-Shaw flows 981

76D33

Waves for incompressible viscous fluids 1285

76D45

Capillarity (surface tension) for incompressible viscous fluids [See also 76B45] 2062

76D50

Stratification effects in viscous fluids 561

76D55

Flow control and optimization for incompressible viscous fluids [See also 49Q10, 93C20, 93C95] 1234

76D99

None of the above, but in this section 3441

76Exx

Hydrodynamic stability 17980

76E05

Parallel shear flows in hydrodynamic stability 2876

76E06

Convection in hydrodynamic stability 1693

76E07

Rotation in hydrodynamic stability 824

76E09

Stability and instability of nonparallel flows in hydrodynamic stability 425

76E15

Absolute and convective instability and stability in hydrodynamic stability 2080

76E17

Interfacial stability and instability in hydrodynamic stability 1876

76E19

Compressibility effects in hydrodynamic stability 67

76E20

Stability and instability of geophysical and astrophysical flows 2338

76E25

Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 2915

76E30

Nonlinear effects in hydrodynamic stability 2762

76E99

None of the above, but in this section 3045

76Fxx

Turbulence [See also 37-XX, 60Gxx, 60Jxx] 20068

76F02

Fundamentals of turbulence 430

76F05

Isotropic turbulence; homogeneous turbulence 2445

76F06

Transition to turbulence 879

76F10

Shear flows and turbulence 3778

76F20

Dynamical systems approach to turbulence [See also 37-XX] 767

76F25

Turbulent transport, mixing 1776

76F30

Renormalization and other field-theoretical methods for turbulence [See also 81T99] 105

76F35

Convective turbulence [See also 76E15, 76Rxx] 505

76F40

Turbulent boundary layers 1401

76F45

Stratification effects in turbulence 374

76F50

Compressibility effects in turbulence 413

76F55

Statistical turbulence modeling [See also 76M35] 1171

76F60

\(k\)-\(\varepsilon\) modeling in turbulence 1076

76F65

Direct numerical and large eddy simulation of turbulence 4158

76F70

Control of turbulent flows 308

76F80

Turbulent combustion; reactive turbulence 0

76F99

None of the above, but in this section 3662

76Gxx

General aerodynamics and subsonic flows 3070

76G25

General aerodynamics and subsonic flows 3050

76G99

None of the above, but in this section 15

76Hxx

Transonic flows 2552

76H05

Transonic flows 2550

76H99

None of the above, but in this section 1

76Jxx

Supersonic flows 2877

76J20

Supersonic flows 2871

76J99

None of the above, but in this section 5

76Kxx

Hypersonic flows 1434

76K05

Hypersonic flows 1432

76K99

None of the above, but in this section 0

76Lxx

Shock waves and blast waves in fluid mechanics [See also 35L67] 7359

76L05

Shock waves and blast waves in fluid mechanics [See also 35L67] 7347

76L99

None of the above, but in this section 8

76Mxx

Basic methods in fluid mechanics [See also 65-XX] 68669

76M10

Finite element methods applied to problems in fluid mechanics 12389

76M12

Finite volume methods applied to problems in fluid mechanics 6996

76M15

Boundary element methods applied to problems in fluid mechanics 2393

76M20

Finite difference methods applied to problems in fluid mechanics 12557

76M21

Inverse problems in fluid mechanics 4

76M22

Spectral methods applied to problems in fluid mechanics 2069

76M23

Vortex methods applied to problems in fluid mechanics 424

76M27

Visualization algorithms applied to problems in fluid mechanics 221

76M28

Particle methods and lattice-gas methods 3643

76M30

Variational methods applied to problems in fluid mechanics 1493

76M35

Stochastic analysis applied to problems in fluid mechanics 2118

76M40

Complex variables methods applied to problems in fluid mechanics 477

76M45

Asymptotic methods, singular perturbations applied to problems in fluid mechanics 2657

76M50

Homogenization applied to problems in fluid mechanics 527

76M55

Dimensional analysis and similarity applied to problems in fluid mechanics 724

76M60

Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics 725

76M99

None of the above, but in this section 11193

76Nxx

Compressible fluids and gas dynamics, general 17625

76N06

Compressible Navier-Stokes equations 1

76N10

Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics [See also 35L60, 35L65, 35Q30] 5697

76N15

Gas dynamics, general 8164

76N17

Viscous-inviscid interaction for compressible fluids and gas dynamics 163

76N20

Boundary-layer theory for compressible fluids and gas dynamics 1779

76N25

Flow control and optimization for compressible fluids and gas dynamics 849

76N30

Waves in compressible fluids 0

76N99

None of the above, but in this section 1135

76Pxx

Rarefied gas flows, Boltzmann equation in fluid mechanics [See also 82B40, 82C40, 82D05] 5979

76P05

Rarefied gas flows, Boltzmann equation in fluid mechanics [See also 82B40, 82C40, 82D05] 5965

76P99

None of the above, but in this section 5

76Qxx

Hydro- and aero-acoustics 9436

76Q05

Hydro- and aero-acoustics 9420

76Q99

None of the above, but in this section 10

76Rxx

Diffusion and convection 15149

76R05

Forced convection 2929

76R10

Free convection 6445

76R50

Diffusion [See also 60J60] 3135

76R99

None of the above, but in this section 3501

76Sxx

Flows in porous media; filtration; seepage 18322

76S05

Flows in porous media; filtration; seepage 18268

76S99

None of the above, but in this section 31

76Txx

Multiphase and multicomponent flows 19059

76T06

Liquid-liquid two component flows 2

76T10

Liquid-gas two-phase flows, bubbly flows 4277

76T15

Dusty-gas two-phase flows 813

76T17

Two gas multicomponent flows 1

76T20

Suspensions 2352

76T25

Granular flows [See also 74C99, 74E20] 1024

76T30

Three or more component flows 799

76T99

None of the above, but in this section 8382

76Uxx

Rotating fluids 7448

76U05

General theory of rotating fluids 7437

76U60

Geophysical flows [See also 86A05, 86A10] 1

76U65

Rossby waves [See also 86A05, 86A10] 3

76U99

None of the above, but in this section 3

76Vxx

Reaction effects in flows [See also 80A32] 5880

76V05

Reaction effects in flows [See also 80A32] 5878

76V99

None of the above, but in this section 0

76Wxx

Magnetohydrodynamics and electrohydrodynamics 14675

76W05

Magnetohydrodynamics and electrohydrodynamics 14628

76W99

None of the above, but in this section 16

76Xxx

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 7091

76X05

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 7083

76X99

None of the above, but in this section 3

76Yxx

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2882

76Y05

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2877

76Y99

None of the above, but in this section 2

76Zxx

Biological fluid mechanics [See also 74F10, 74L15, 92Cxx] 4758

76Z05

Physiological flows [See also 92C35] 3605

76Z10

Biopropulsion in water and in air 746

76Z99

None of the above, but in this section 408

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Mathematics Subject Classification – MSC2020

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