Shkoller, Steve
- Well-posedness of the free-surface incompressible Euler equations with or without surface tension
2005/11/09 by Daniel Coutand, Coutand, Daniel, Steve Shkoller +1 · 5 citations
Earth and Planetary Sciences · Mathematics · Engineering · #Aquatic and Environmental Studies #Navier-Stokes equation solutions #Computational Fluid Dynamics and Aerodynamics
- Nonuniqueness of weak solutions to the SQG equation
2016/10/03 by Buckmaster, Tristan, Shkoller, Steve, Vicol, Vlad · 5 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics
- Formation of shocks for 2D isentropic compressible Euler
2019/07/08 by Tristan Buckmaster, Steve Shkoller, Buckmaster, Tristan +3 · 3 citations
Engineering · Mathematics · #35L67 #35Q31 #76L05 #76N15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Navier-Stokes equation solutions
- Formation of point shocks for 3D compressible Euler
2019/12/10 by Buckmaster, Tristan, Shkoller, Steve, Vicol, Vlad · 3 citations
#35L67 #35Q31 #76L05 #76N15 #Analysis of PDEs (math.AP) #FOS: Mathematics
- Shock formation and vorticity creation for 3d Euler
2020/06/26 by Buckmaster, Tristan, Shkoller, Steve, Vicol, Vlad · 3 citations
#35L67 #35Q31 #76L05 #76N15 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
- Solvability and regularity for an elliptic system prescribing the curl, divergence, and partial trace of a vector field on Sobolev-class domains
2014/08/11 by Cheng, C. H. Arthur, Shkoller, Steve · 2 citations
#35J57 #58A14 #Analysis of PDEs (math.AP) #FOS: Mathematics
- Well-posedness of the Muskat problem with H2 initial data
2014/12/24 by C. H. Arthur Cheng, Rafael Granero-Belinchón, Cheng, C. H. Arthur +3 · 2 citations
Mathematics · #35Q35 #35R35 #35S10 #76B03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
- Global existence of near-affine solutions to the compressible Euler equations
2017/10/23 by Shkoller, Steve, Sideris, Thomas C. · 2 citations
#35B35 #35L65 #35Q31 #76N10 #76N15 #Analysis of PDEs (math.AP) #FOS: Mathematics
- Multisymplectic geometry, variational integrators, and nonlinear PDEs
1998/07/15 by Marsden, Jerrold E., Patrick, George W., Shkoller, Steve · 1 citation
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Symplectic Geometry (math.SG)
- Discrete Euler-Poincaré and Lie-Poisson Equations
1999/09/17 by Marsden, Jerrold E., Pekarsky, Sergey, Shkoller, Steve · 1 citation
#58B20 #58D05 #76E99 #FOS: Mathematics #Numerical Analysis (math.NA) #Symplectic Geometry (math.SG)
- Well-posedness in smooth function spaces for the moving-boundary 1-D compressible Euler equations in physical vacuum
2009/10/16 by Coutand, Daniel, Shkoller, Steve · 1 citation
#35L65 #35L70 #35L80 #35Q35 #35R35 #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics
- Well-posedness for the classical Stefan problem and the zero surface tension limit
2011/12/26 by Hadzic, Mahir, Shkoller, Steve · 1 citation
#35K55 #35Q79 #Analysis of PDEs (math.AP) #FOS: Mathematics
- Well-posedness of the free-boundary compressible 3-D Euler equations\n with surface tension and the zero surface tension limit
2012/08/13 by Daniel Coutand, Jason Hole, Coutand, Daniel +3 · 1 citation
Mathematics · Earth and Planetary Sciences · #Navier-Stokes equation solutions #Aquatic and Environmental Studies #Advanced Mathematical Physics Problems
- Global stability and decay for the classical Stefan problem
2012/12/06 by Hadžić, Mahir, Shkoller, Steve · 1 citation
#35B65 #35K05 #35R35 #80A22 #Analysis of PDEs (math.AP) #FOS: Mathematics
- On the splash singularity for the free-surface of a Navier-Stokes fluid
2015/05/08 by Coutand, Daniel, Shkoller, Steve · 1 citation
#35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics
- The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions
2023/10/12 by Shkoller, Steve, Vicol, Vlad · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
- Rigorous Asymptotic Models of Water Waves
2018/06/30 by Cheng, C. H. Arthur, Granero-Belinchon, Rafael, Shkoller, Steve +1 · 1 citation
#35C20 #65N35 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA)
- Simultaneous development of shocks and cusps for 2D Euler with azimuthal symmetry from smooth data
2021/06/03 by Buckmaster, Tristan, Drivas, Theodore D., Shkoller, Steve +1 · 1 citation
#35L67 #35Q31 #76L05 #76N15 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph)
- A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy
2023/02/02 by Isaac Neal, Steve Shkoller, Neal, Isaac +3 · 1 citation
Mathematics · Physics and Astronomy · #Navier-Stokes equation solutions #Nonlinear Waves and Solitons
- A new type of stable shock formation in gas dynamics
2023/03/29 by Neal, Isaac, Rickard, Calum, Shkoller, Steve +1 · 1 citation
#35L67 #76L05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
- Vorticity blowup in 2D compressible Euler equations
2024/07/08 by Chen, Jiajie, Cialdea, Giorgio, Shkoller, Steve +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)