Our proof is based on Serfaty's modulated-energy method, but compared to that of Han-Kwan and Iacobelli, crucially uses an improved "renormalized commutator" estimate to obtain the larger range forθ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{ams...
Learn how to define Newton's second law of motion. Discover all the equations associated with Newton's second law of motion, along with experiments...
When we applied this method to nonlinear Klein-Gordon equation, we derived relativistic Newton's law and Einstein's formula for inertial mass. Here we apply the same approach to nonlinear Schrodinger equation and derive non-relativistic Newton's law for the trajectory of concentration. Full-Text ...
This chapter develops the earliest important examples of differential equations, which in fact are connected with the origins of calculus. These equations were used by Newton to derive and unify the three laws of Kepler. These laws were found from the earlier astronomical observations of Tycho ...
Rebilas, KrzysztofApeiron: Studies in Infinite Nature
Physics - Classical PhysicsStarting from the classical Newton's second law which, according to ourassumption, is valid in any instantaneous inertial rest frame of body thatmoves in Minkowskian space-time we get the relativistic equation of motion$\\vec{F}=d\\vec{p}/dt$, where $\\vec{p}...
Starting from the classical Newton's second law which, according to our\nassumption, is valid in any instantaneous inertial rest frame of body that\nmoves in Minkowskian space-time we get the relativistic equation of motion\n$\\vec{F}=d\\vec{p}/dt$, where $\\vec{p}$ is the ...
N. Ayi, From Newton's law to the linear Boltzmann equation without cut-off, accepted for publication, Comm. Math. Phys.N. Ayi. From Newton's Law to the Linear Boltzmann Equation Without Cut-Off. Commu- nications in Mathematical Physics, 350(3):1219-1274, 2017....
The field equation from Newton’s law of motion and the absence of magnetic monopole - Singh, Dadhich () Citation Context ...of the equations. This gave rise to considerable activity in this direction involving rederivations, generalizations and extensions. However the attention centred on the ...
Recently, Han-Kwan and Iacobelli (Proc Am Math Soc 149:3045-3061, 2021) showed that in the monokinetic regime, one can directly obtain the Euler equation from a system of N particles interacting in T-d, d >= 2, via Newton's second law through a supercritical meanffield limit. Namely...