zbMATH — the first resource for mathematics

Mathematics Subject Classification – MSC2010

76-XX

Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX] 211721

76-00

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

76-01

Instructional exposition (textbooks, tutorial papers, etc.) 797

76-02

Research exposition (monographs, survey articles) 3724

76-03

Historical (must also be assigned at least one classification number from Section 01) 438

76-04

Explicit machine computation and programs (not the theory of computation or programming) 993

76-05

Experimental work 4553

76-06

Proceedings, conferences, collections, etc. 3035

76Axx

Foundations, constitutive equations, rheology 15611

76A02

Foundations of fluid mechanics 1095

76A05

Non-Newtonian fluids 5973

76A10

Viscoelastic fluids 4592

76A15

Liquid crystals [See also 82D30] 990

76A20

Thin fluid films 1564

76A25

Superfluids (classical aspects) 182

76A99

None of the above, but in this section 1674

76Bxx

Incompressible inviscid fluids 25550

76B03

Existence, uniqueness, and regularity theory [See also 35Q35] 1116

76B07

Free-surface potential flows 646

76B10

Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 5004

76B15

Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 9786

76B20

Ship waves 615

76B25

Solitary waves [See also 35C11] 1938

76B45

Capillarity (surface tension) [See also 76D45] 1104

76B47

Vortex flows 3563

76B55

Internal waves 1175

76B60

Atmospheric waves [See also 86A10] 543

76B65

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

76B70

Stratification effects in inviscid fluids 484

76B75

Flow control and optimization [See also 49Q10, 93C20, 93C95] 349

76B99

None of the above, but in this section 1900

76Dxx

Incompressible viscous fluids 40823

76D03

Existence, uniqueness, and regularity theory [See also 35Q30] 2751

76D05

Navier-Stokes equations [See also 35Q30] 18894

76D06

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

76D07

Stokes and related (Oseen, etc.) flows 4613

76D08

Lubrication theory 1415

76D09

Viscous-inviscid interaction 177

76D10

Boundary-layer theory, separation and reattachment, higher-order effects 5934

76D17

Viscous vortex flows 1236

76D25

Wakes and jets 1567

76D27

Other free-boundary flows; Hele-Shaw flows 905

76D33

Waves 1206

76D45

Capillarity (surface tension) [See also 76B45] 1880

76D50

Stratification effects in viscous fluids 504

76D55

Flow control and optimization [See also 49Q10, 93C20, 93C95] 1103

76D99

None of the above, but in this section 3391

76Exx

Hydrodynamic stability 17314

76E05

Parallel shear flows 2735

76E06

Convection 1590

76E07

Rotation 775

76E09

Stability and instability of nonparallel flows 404

76E15

Absolute and convective instability and stability 2010

76E17

Interfacial stability and instability 1759

76E19

Compressibility effects 59

76E20

Stability and instability of geophysical and astrophysical flows 2285

76E25

Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 2855

76E30

Nonlinear effects 2647

76E99

None of the above, but in this section 3008

76Fxx

Turbulence [See also 37-XX, 60Gxx, 60Jxx] 18409

76F02

Fundamentals 369

76F05

Isotropic turbulence; homogeneous turbulence 2290

76F06

Transition to turbulence 722

76F10

Shear flows 3578

76F20

Dynamical systems approach to turbulence [See also 37-XX] 711

76F25

Turbulent transport, mixing 1617

76F30

Renormalization and other field-theoretical methods [See also 81T99] 99

76F35

Convective turbulence [See also 76E15, 76Rxx] 419

76F40

Turbulent boundary layers 1112

76F45

Stratification effects 303

76F50

Compressibility effects 360

76F55

Statistical turbulence modeling [See also 76M35] 1092

76F60

$k$-$\varepsilon$ modeling 1010

76F65

Direct numerical and large eddy simulation of turbulence 3430

76F70

Control of turbulent flows 250

76F99

None of the above, but in this section 3598

76Gxx

General aerodynamics and subsonic flows 2824

76G25

General aerodynamics and subsonic flows 2802

76G99

None of the above, but in this section 15

76Hxx

Transonic flows 2495

76H05

Transonic flows 2494

76H99

None of the above, but in this section 1

76Jxx

Supersonic flows 2761

76J20

Supersonic flows 2754

76J99

None of the above, but in this section 4

76Kxx

Hypersonic flows 1365

76K05

Hypersonic flows 1365

76K99

None of the above, but in this section 0

76Lxx

Shock waves and blast waves [See also 35L67] 6978

76L05

Shock waves and blast waves [See also 35L67] 6966

76L99

None of the above, but in this section 8

76Mxx

Basic methods in fluid mechanics [See also 65-XX] 64303

76M10

Finite element methods 11248

76M12

Finite volume methods 6213

76M15

Boundary element methods 2201

76M20

Finite difference methods 11954

76M22

Spectral methods 1880

76M23

Vortex methods 391

76M25

Other numerical methods 11295

76M27

Visualization algorithms 194

76M28

Particle methods and lattice-gas methods 3152

76M30

Variational methods 1410

76M35

Stochastic analysis 2012

76M40

Complex-variables methods 462

76M45

Asymptotic methods, singular perturbations 2546

76M50

Homogenization 495

76M55

Dimensional analysis and similarity 694

76M60

Symmetry analysis, Lie group and algebra methods 663

76M99

None of the above, but in this section 11030

76Nxx

Compressible fluids and gas dynamics, general 16534

76N10

Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 5376

76N15

Gas dynamics, general 7606

76N17

Viscous-inviscid interaction 146

76N20

Boundary-layer theory 1698

76N25

Flow control and optimization 791

76N99

None of the above, but in this section 1096

76Pxx

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5744

76P05

Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 5737

76P99

None of the above, but in this section 5

76Qxx

Hydro- and aero-acoustics 8968

76Q05

Hydro- and aero-acoustics 8956

76Q99

None of the above, but in this section 9

76Rxx

Diffusion and convection 14615

76R05

Forced convection 2799

76R10

Free convection 6212

76R50

Diffusion [See also 60J60] 2971

76R99

None of the above, but in this section 3463

76Sxx

Flows in porous media; filtration; seepage 17116

76S05

Flows in porous media; filtration; seepage 17070

76S99

None of the above, but in this section 32

76Txx

Two-phase and multiphase flows 17821

76T10

Liquid-gas two-phase flows, bubbly flows 3771

76T15

Dusty-gas two-phase flows 747

76T20

Suspensions 1985

76T25

Granular flows [See also 74C99, 74E20] 924

76T30

Three or more component flows 733

76T99

None of the above, but in this section 8223

76Uxx

Rotating fluids 7062

76U05

Rotating fluids 7055

76U99

None of the above, but in this section 4

76Vxx

Reaction effects in flows [See also 80A32] 5642

76V05

Reaction effects in flows [See also 80A32] 5638

76V99

None of the above, but in this section 0

76Wxx

Magnetohydrodynamics and electrohydrodynamics 13818

76W05

Magnetohydrodynamics and electrohydrodynamics 13780

76W99

None of the above, but in this section 15

76Xxx

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6958

76X05

Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 6950

76X99

None of the above, but in this section 3

76Yxx

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2715

76Y05

Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 2709

76Y99

None of the above, but in this section 2

76Zxx

Biological fluid mechanics [See also 74F10, 74L15, 92Cxx] 4301

76Z05

Physiological flows [See also 92C35] 3275

76Z10

Biopropulsion in water and in air 619

76Z99

None of the above, but in this section 390

Overview

General mathematics

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

Field theory and polynomials

Commutative algebra

Algebraic geometry

Linear and multilinear algebra; matrix theory

Associative rings and algebras

Nonassociative rings and algebras

Category theory, homological algebra

$K$-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximation and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

Functional analysis

Operator theory

Calculus of variations and optimal control; optimization

Geometry

Convex and discrete geometry

Differential geometry

General topology

Algebraic topology

Manifolds and cell complexes

Global analysis, analysis on manifolds

Probability theory and stochastic processes

Statistics

Numerical analysis

Computer science

Mechanics of particles and systems

Mechanics of deformable solids

Fluid mechanics

Optics, electromagnetic theory

Classical thermodynamics, heat transfer

Quantum Theory

Statistical mechanics, structure of matter

Relativity and gravitational theory

Astronomy and astrophysics

Geophysics

Operations research, mathematical programming

Game theory, economics, social and behavioral sciences

Biology and other natural sciences

Systems theory; control

Information and communication, circuits

Mathematics education

any	anywhere
cc	classification code
ct	classification text

a & b	logical and	abc*	right wildcard
a \| b	logical or	"ab c"	phrase
!ab	logical not	(ab c)	parentheses

zbMATH — the first resource for mathematics

Examples

Fields

Operators

Mathematics Subject Classification – MSC2010

Overview