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Results tagged with ap.analysis-of-pdes
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user 32389
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
Schrodinger equation with magnetic vector potential
Maybe the following references will be helpful:
http://link.springer.com/article/10.1007%2FBF01682741 (Remarks on schrödinger operators with vector potentials, by Tosio Kato),
https://projecteuclid.or …
- 16.5k
0
votes
Does the Riemann-Christoffel curvature determine the connection?
It seems a partial answer (the solution is found with some additional restrictions)
is given in the paper http://link.springer.com/article/10.1007%2FBF00759087 (Determination of the metric from the cu …
- 16.5k
4
votes
Accepted
Classical theory for the incompressible Euler equation (reference request)
Classical existence and regularity results can be found in the survey http://arxiv.org/abs/math/0703406 (Euler Equations of Incompressible Ideal Fluids, by C. Bardos and E. S. Titi -- http://www.mccme …
- 16.5k
3
votes
Looking for an interesting result on the Navier-Stokes equations
Maybe the following papers will be helpful: Some open questions in hydrodynamics and Between Hydrodynamics and Elasticity Theory: The First Five Births of the Navier-Stokes Equation.
Another option wo …
- 16.5k
0
votes
Solution to Schrödinger equation
In the linear case, $V(x)=x$, the Schrodinger equation can be solved by Lewis-Riesenfeld approach. See http://link.springer.com/article/10.1007%2Fs12648-013-0322-4 as well as http://arxiv.org/abs/quan …
- 16.5k
2
votes
What are the applications of Grillakis Shatah and Strauss paper?
Maybe the following review article http://www.ams.org/journals/bull/2009-46-01/S0273-0979-08-01228-7/home.html (Why are solitons stable? by Terence Tao) will be helpful.
Some applications of the soli …
- 16.5k
-1
votes
Textbooks for PDE between Strauss and Folland
Stanley J. Farlow's "Partial Differential Equations for Scientists and Engineers" (http://www.amazon.com/Differential-Equations-Scientists-Engineers-Mathematics/dp/048667620X) is very unusual textboo …
4
votes
Reference for Feynman-Kac
A rigorous treatment of the Feynman-Kac formula is given in the chapter 3 of the book "Quantum Physics: A Functional Integral Point of View" by J. Glimm and A. Jaffe: http://www.springer.com/in/book/ …
- 16.5k
1
vote
Quantum Mechanics and bilinear optimal control theory
In addition to the literature indicated by Carlo Beenakker: in this 2015 review http://arxiv.org/abs/1508.00442 (Training Schrödinger's cat: quantum optimal control, by S.J. Glaser et al.) the authors …
- 16.5k
4
votes
Alternative proof of Varadhan's formula on Riemann manifolds
Varadhan's result was extended to wider class of operators and manifolds by Molchanov: http://iopscience.iop.org/0036-0279/30/1/R01 (Diffusion processes and Riemannian geometry). See also http://arxiv …
- 16.5k
1
vote
References on thin film equation: derivation and properties
Earlier references on derivation of this equation can be found in
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-the-motion-of-a-small-viscous-droplet-that-wets-a-surfa …
- 16.5k