Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations
Euler equations (fluid dynamics) 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Euler_equations_(fluid_dynamics)" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Euler_equations_(fluid_dynamic...</a><p>&gt; <i>In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler.</i> In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. [1]<p>Navier–Stokes equations 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Navier–Stokes_equations" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Navier–Stokes_equation...</a><p>&gt; <i>The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass </i> for Newtonian fluids.<p>Computational fluid dynamics 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Computational_fluid_dynamics" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Computational_fluid_dynamics</a><p>Numerical methods in fluid mechanics 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Numerical_methods_in_fluid_mechanics" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Numerical_methods_in_fluid_mec...</a><p>- [ ] Quantum fluid 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Quantum_fluid" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Quantum_fluid</a><p>&gt; <i>Quantum mechanical effects become significant for physics in the range of the de Broglie wavelength. For condensed matter, this is when the de Broglie wavelength of a particle is greater than the spacing between the particles in the</i> lattice <i>that comprises the matter.</i> [...]<p>&gt; <i>The above temperature limit T has different meaning depending on the quantum statistics followed by each system, but generally refers to the point at which the system manifests quantum fluid properties. For a system of fermions, T is an estimation of the Fermi energy of the system, where processes important to phenomena such as superconductivity take place. For bosons, T gives an estimation of the Bose-Einstein condensation temperature.</i><p>Classical fluid <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Classical_fluid" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Classical_fluid</a><p>&gt; <i>Classical fluids [1] are systems of particles which retain</i> a definite volume, <i>and are at sufficiently high temperatures (compared to their Fermi energy) that quantum effects can be neglected</i> [...] <i>Common liquids, e.g., liquid air, gasoline etc., are essentially mixtures of classical fluids. Electrolytes, molten salts, salts dissolved in water, are classical charged fluids. A classical fluid when cooled undergoes a freezing transition. On heating it undergoes an evaporation transition and becomes a classical gas that obeys Boltzmann statistics.</i><p>Chaos theory <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Chaos_theory" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Chaos_theory</a><p>&gt; <i>Chaos theory is [...] focused on underlying patterns and deterministic laws highly sensitive to initial conditions in dynamical systems that were thought to have completely random states of disorder and irregularities. [1] Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, and self-organization.</i><p>Quantum chaos 
<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Quantum_chaos" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Quantum_chaos</a><p>&gt; <i>If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics?</i><p>... in dynamic, nonlinear - possibly adaptive - complex systems.