Blow-up of solutions to the generalized inviscid Proudman-Johnson equation
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Publication:368437
DOI10.1007/s00021-012-0126-xzbMath1277.35077arXiv1306.4437OpenAlexW3105975776MaRDI QIDQ368437
Alejandro Sarria, Ralph Saxton
Publication date: 23 September 2013
Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1306.4437
Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Periodic solutions to PDEs (35B10) Blow-up in context of PDEs (35B44)
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Cites Work
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- The generalized Proudman-Johnson equation revisited
- The periodic Cauchy problem of the modified Hunter-Saxton equation
- Global and singular solutions to the generalized Proudman-Johnson equation
- Well-posedness of the generalized Proudman-Johnson equation without viscosity
- On the inviscid Proudman-Johnson equation
- Some similarity solutions of the Navier-Stokes equations and related topics
- Euler equations on homogeneous spaces and Virasoro orbits
- On a nonlinear hyperbolic variational equation: I. Global existence of weak solutions. II: The zero-viscosity and dispersion limits
- Global weak solutions to the generalized Proudman-Johnson equation
- Weak geodesic flow and global solutions of the Hunter-Saxton equation
- On the differential equations of the simplest boundary-layer problems
- GENERALIZED CHARACTERISTICS AND THE HUNTER–SAXTON EQUATION
- A Solvable Nonlinear Wave Equation
- Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form
- Dynamics of Director Fields
- On the Structure of Solutions to the Periodic Hunter--Saxton Equation
- Global Existence of Some Infinite Energy Solutions for a Perfect Incompressible Fluid
- Global Solutions of the Hunter--Saxton Equation
- Boundary-layer growth near a rear stagnation point