
There is a problem with this kind of question, namely for many mathematicians the most interesting mathematical physics is a new vast area on the interface of quantum field theory and geometry/topology emerging from about late 1960s till now. You will find no word on this new mathematical physics in the classical books like ReedSimon, MorseFeshbach (Methods of mathematical physics, 1953 and later ed.), Vladimirov (Equations of mathematical physics) and even older CourantHilbert which focus on the integral and differential equations of mathematical physics, special functions, generalized functions (distributions), representations of classical groups and functional analysis. For your classical hydrodynamics indeed the classical textbooks and reference books suffice, but for people interested in a bit more modern mathematical physics we could add (in various level of exposition and specialization)
Yvonne ChoquetBruhat, Cecile DewittMorette, Analysis, manifolds and physics, 1982 and 2001
Albert Schwartz, Quantum field theory and topology, Grundlehren der Math. Wissen. 307, Springer 1993. (translated from Russian original)
Bernard F. Schutz, Geometrical methods of mathematical physics (elementary intro)
Eberhard Zeidler, Quantum field theory. A bridge between mathematicians and physicists. I: Basics in mathematics and physics. , II: Quantum electrodynamics
Charles Nash, Differential topology and quantum field theory, Acad. Press 1991.
P. Deligne, P. Etingof, D.S. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D.R. Morrison and E. Witten, eds. Quantum fields and strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version)
Gregory L. Naber, Topology, geometry, and gauge fields: interactions
Mikio Nakahara, Geometry, topology and physics
Peter Olver, Equivalence, invariants, and symmetry, Cambridge University Press, Cambridge, UK, 1995.
James Glimm, Arthur Jaffe, Quantum physics: a functional integral point of view, Springer
Sternberg, Shlomo (1994), Group theory and physics, Cambridge University Press.
V. I. Arnold, Mathematical methods of classical mechanics, Springer (1989).
V. Guillemin, S. Sternberg, Symplectic techniques in physics, Cambridge University Press (1990)
Leon A. Takhtajan, Quantum mechanics for mathematicians, Graduate Studies in Mathematics 95, Amer. Math. Soc. 2008.
Marian Fecko, Differential geometry and Lie groups for physicists
V. S. Varadarajan, Supersymmetry for mathematicians: an introduction, AMS and Courant Institute, 2004.
R. E. Borcherds, A. Barnard, Lectures on QFT, arxiv:mathph/0204014
Paul Aspinwall, Tom Bridgeland, Alastair Craw, Michael R. Douglas, Mark Gross, Dirichlet branes and mirror symmetry, Amer. Math. Soc. Clay Math. Institute 2009.
R. S. Ward, R. O. Wells, Twistor geometry and field theory (CUP, 1990)
N. N. Bogoliubov, A. A. Logunov, I. T. Todorov, Introduction to axiomatic quantum field theory, 1975
O. Babelon, D. Bernard, M. Talon, Introduction to classical integrable systems, Cambridge Univ. Press 2003.
Martin Schottenloher, A mathematical introduction to conformal field theory
Philippe Di Francesco,Pierre Mathieu,David Sénéchal, Conformal field theory, Springer 1997
T. Miwa, M. Jimbo, E. Date, Solitons: Differential equations, symmetries and infinite dimensional algebras, Cambridge Tracts in Mathematics 135, translated from Japanese by Miles Reid
V. Kac, Vertex algebras for beginners, Amer. Math. Soc.
Ludwig D. Faddeev, Leon Takhtajan, Hamiltonian methods in the theory of solitons, Springer
V.E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum inverse scattering method and correlation functions, Cambridge Univ. Press 1997.
N. P. Landsman, Mathematical topics between classical and quantum mechanics, Springer Monographs in Mathematics 1998. xx+529 pp.
Sean Bates, Alan Weinstein, Lectures on the geometry of quantization, pdf
A. Cannas da Silva, A. Weinstein, Geometric models for noncommutative algebras, 1999, pdf
I have placed these references in new nlab entry books and reviews in mathematical physics which will be updated at times wuth more specialized references.
