Khesin - Topological methods in hydrodynamics , Applied Mathematical Sciences, vol. MR Zbl Titi - Euler equations for an ideal incompressible fluid , Uspekhi Mat. Nauk 62 , p. Surveys 62 , p. Nauk SSSR , p.

Flores - On total differential inclusions , Rend. Padova 92 , p.

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## homotopy theory - H-principle and PDE's - MathOverflow

Constantin , S. Shvydkoy - Energy conservation and Onsager's conjecture for the Euler equations , Nonlinearity 21 , p. Article MR Zbl Constantin , W. Titi - Onsager's conjecture on the energy conservation for solutions of Euler's equation , Comm.

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Constantin , C. Majda - Geometric constraints on potentially singular solutions for the 3-D Euler equations , Comm.

Partial Differential Equations 21 , p. Conti , C.

Marcellini - General existence theorems for Hamilton- Jacobi equations in the scalar and vectorial cases , Acta Math. Marcellini , Implicit partial differential equations , Progress in Nonlinear Differential Equations and their Applications, vol.

## Convex Integration Theory: Solutions to the H-Principle in Geometry and Topology

Pisante - A general existence theorem for differential inclusions in the vector valued case , Port. Pianigiani - A Baire category approach to the existence of solutions of multivalued differential equations in Banach spaces , Funkcial. Delort - Existence de nappes de tourbillon en dimension deux , J. Each method has its own distinct foundation, based on an independent geometrical or analytical insight. Con- quently, each method has a range of applications to problems in topology that are best suited to its particular insight. For example, a distinguishing feature of ConvexIntegrationtheoryisthatitappliestosolveclosed relationsinjetspaces, including certain general classes of underdetermined non-linear systems of par- 1 tial di?

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As a case of interest, the Nash-Kuiper C -isometric immersion theorem can be reformulated and proved using Convex Integration theory cf. Gromov [18]. No such results on closed relations in jet spaces can be proved by means of the other two methods. On the other hand, many classical results in immersion-theoretic topology, such as the classi? The covering homotopy method is due originally to S. Smale [36] who proved a crucial covering homotopy result in order to solve the classi?

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These general methods are not linearly related in the sense that succ- sive methods subsumed the previous methods. Each method has its own distinct foundation, based on an independent geometrical or analytical insight. Con- quently, each method has a range of applications to problems in topology that are best suited to its particular insight.