Spectral theory of pseudodifferential operators of degree 0 and an application to forced linear waves
Copyright policy )Spectral theory of pseudodifferential operators of degree 0 and an application to forced linear waves
We extend the results of our paper "Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0" written with Laure Saint-Raymond to the case of forced linear wave equations in any dimension. We prove that, in dimension 2,if the foliation on the boundary at infinity of the energy shell is Morse-Smale, we can apply Mourre's theory and hence get the asymptotics of the forced solution. We also characterize the wavefrontsets of the limit Schwartz distribution using radial propagation estimates.
Internal waves for incompressible inviscid fluids, attractors, FOS: Physical sciences, PDEs in connection with fluid mechanics, 35B34, 510, Mathematics - Spectral Theory, Mourre theory, Mathematics - Analysis of PDEs, inertial waves, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], forced waves, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Resonance in context of PDEs, escape functions, limiting absorption principle, Spectral Theory (math.SP), Mathematical Physics, AMS codes: 35Q30, pseudodifferential operator, Pseudodifferential operators as generalizations of partial differential operators, 58J40, Morse-Smale property, spectral theory, Mathematical Physics (math-ph), pseudo-differential operator, Morse–Smale property, Stratification effects in inviscid fluids, 76B55, internal waves, 35Q30, Pseudodifferential and Fourier integral operators on manifolds, Navier-Stokes equations, 76B70, 35Q35, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP], Analysis of PDEs (math.AP)
Internal waves for incompressible inviscid fluids, attractors, FOS: Physical sciences, PDEs in connection with fluid mechanics, 35B34, 510, Mathematics - Spectral Theory, Mourre theory, Mathematics - Analysis of PDEs, inertial waves, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], forced waves, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Resonance in context of PDEs, escape functions, limiting absorption principle, Spectral Theory (math.SP), Mathematical Physics, AMS codes: 35Q30, pseudodifferential operator, Pseudodifferential operators as generalizations of partial differential operators, 58J40, Morse-Smale property, spectral theory, Mathematical Physics (math-ph), pseudo-differential operator, Morse–Smale property, Stratification effects in inviscid fluids, 76B55, internal waves, 35Q30, Pseudodifferential and Fourier integral operators on manifolds, Navier-Stokes equations, 76B70, 35Q35, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP], Analysis of PDEs (math.AP)
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