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Tao's mathematical knowledge has an extraordinary combination of breadth and depth: he can write confidently and authoritatively on topics as diverse as partial differential equations, analytic number theory, the geometry of 3-manifolds, nonstandard analysis, group theory, model theory, quantum mechanics, probability, ergodic theory ...
In mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...
In the context of partial differential equations, it is called the Schwarz integrability condition. Formal expressions of symmetry ... Tao, Terence (2006), ...
The mathematical analysis of partial differential equations uses analytical techniques to study partial differential equations. The subject has connections to and motivations from physics and differential geometry, the latter through the branches of global and geometric analysis .
142 Higher Order Fourier Analysis, Terence Tao (2012, ISBN 978-0-8218-8986-2) 143 Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations, Alberto Bressan (2013, ISBN 978-0-8218-8771-4) 144 Dualities and Representations of Lie Superalgebras, Shun-Jen Cheng, Weiqiang Wang (2012, ISBN 978-0-8218-9118-6)
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. [ 21 ] [ 22 ] [ 23 ] Differential equations play a prominent role in engineering , physics , economics , biology , and other disciplines.
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
Staffilani is a frequent collaborator with James Colliander, Markus Keel, Hideo Takaoka, and Terence Tao, forming a group known as the "I-team". [5] [8] The name of this group has been said to come from the notation for a mollification operator used in the team's method of almost conserved quantities, [9] or as an abbreviation for "interaction", referring both to the teamwork of the group and ...