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42 relations: Acta Mathematica, Clay Mathematics Institute, Conservation of mass, Continuity equation, Continuum mechanics, Density, Divergence, Energy, Fluid, Fluid mechanics, Fractional part, Gifted (film), Gradient, Incompressible flow, Initial condition, Jean Leray, Journal of the American Mathematical Society, Kinetic energy, Laplace operator, List of unsolved problems in physics, Luis Caffarelli, Mathematics, Mean free path, Millennium Prize Problems, Multi-index notation, Navier–Stokes equations, Newton's laws of motion, Newtonian fluid, Nonlinear system, Partial differential equation, Quotient space (topology), Rarefaction, Smoothness, Solenoidal vector field, Terence Tao, Turbulence, United States dollar, Vector field, Viscosity, Vorticity equation, Weak solution, Yakov Sinai.
Acta Mathematica
Acta Mathematica is a peer-reviewed open-access scientific journal covering research in all fields of mathematics.
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Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.
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Conservation of mass
The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system's mass cannot change, so quantity cannot be added nor removed.
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Continuity equation
A continuity equation in physics is an equation that describes the transport of some quantity.
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Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
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Density
The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume.
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Divergence
In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.
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Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
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Fluid
In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress.
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Fluid mechanics
Fluid mechanics is a branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
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Fractional part
The fractional part or decimal part of a non‐negative real number x is the excess beyond that number's integer part.
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Gifted (film)
Gifted is a 2017 American drama film directed by Marc Webb and written by Tom Flynn.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Incompressible flow
In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity.
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Initial condition
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t.
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Jean Leray
Jean Leray (7 November 1906 – 10 November 1998) was a French mathematician, who worked on both partial differential equations and algebraic topology.
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Journal of the American Mathematical Society
The Journal of the American Mathematical Society (JAMS), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society.
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Kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
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Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
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List of unsolved problems in physics
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.
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Luis Caffarelli
Luis Angel Caffarelli (born December 8, 1948) is an Argentine mathematician and luminary in the field of partial differential equations and their applications.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Mean free path
In physics, the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties.
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Millennium Prize Problems
The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.
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Multi-index notation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
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Navier–Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
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Newton's laws of motion
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.
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Newtonian fluid
In continuum mechanics, a Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate—the rate of change of its deformation over time.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Quotient space (topology)
In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.
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Rarefaction
Rarefaction is the reduction of an item's density, the opposite of compression.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Solenoidal vector field
In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a '''transverse vector field''') is a vector field v with divergence zero at all points in the field.
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Terence Tao
Terence Chi-Shen Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics.
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Turbulence
In fluid dynamics, turbulence or turbulent flow is any pattern of fluid motion characterized by chaotic changes in pressure and flow velocity.
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United States dollar
The United States dollar (sign: $; code: USD; also abbreviated US$ and referred to as the dollar, U.S. dollar, or American dollar) is the official currency of the United States and its insular territories per the United States Constitution since 1792.
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Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
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Viscosity
The viscosity of a fluid is the measure of its resistance to gradual deformation by shear stress or tensile stress.
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Vorticity equation
The vorticity equation of fluid dynamics describes evolution of the vorticity of a particle of a fluid as it moves with its flow, that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity).
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Weak solution
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense.
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Yakov Sinai
Yakov Grigorevich Sinai (Я́ков Григо́рьевич Сина́й; born September 21, 1935) is a mathematician known for his work on dynamical systems.
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References
[1] https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
